PISCES-2ET and Its Application Subsystems - Stanford Technology ...

PISCES-2ET and Its 

Application Subsystems 

PART I: 

PART II: 

PISCES-2ET 2D Device Simulator 

Z. Yu, D. Chen, L. So, and R. W. Dutton 

Curve Tracer 

S. G. Beebe, Z. Yu, R. J. G. Goossens, and 

R. W. Dutton 

PART III: Mixed-Mode Device/Circuit Simulator 

F. M. Rotella, Z. Yu, and R. W. Dutton 

Integrated Circuits Laboratory 

Stanford University 

Stanford, California 94305

Copyright 1994 

by The Board of Trustees of Leland Stanford 

Junior University. 

All rights reserved. 

SUPREM, SUPREM-III, SUPREM-IV, and 

PISCES, PISCES-II, PISCES-2ET are registered 

trademarks of Stanford University.

Table of Contents 


PART I 


1 Introduction and Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . .1 

2 DUET Carrier Transport Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 

2.1 Boltzmann Transport Equation and Distribution Function. . . . . . . . . . . . . .6 

2.2 Energy Balance and Thermal Diffusion Equations . . . . . . . . . . . . . . . . . . .7 

2.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 

3 Physical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 

3.1 Mobility Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 

3.1.1 Low field Mobility Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

3.1.2 Mobility Reduction due to Transverse Field . . . . . . . . . . . . . . . . . . . . . . . . 18 

3.1.3 Mobility Dependency on Longitudinal Field/Carrier Temperature. . . . . . . 24 

3.2 Thermal Conductivity Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 

3.3 Recombination and Generation Mechanisms . . . . . . . . . . . . . . . . . . . . . . .28 

3.3.1 Impact Ionization Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 

3.3.2 Photo-Generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

3.3.3 SRH Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

3.3.4 Auger Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 

4 Material Properties for Heterostructures . . . . . . . . . . . . . . . . . . . . .33 

4.1 Material Parameters for Device Simulation . . . . . . . . . . . . . . . . . . . . . . . .33 

4.2 Interpolation Scheme for Composition Dependence . . . . . . . . . . . . . . . . .34 

4.3 Data for Material Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 

4.3.1 Parameters for Base Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 

4.4 Band Structure Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 

4.4.1 Bandgap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 

4.4.2 Electron Affinity and Band-edge Offsets. . . . . . . . . . . . . . . . . . . . . . . . . . . 38 

4.4.3 Effective Mass and Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 

PISCES-2ET and Its Application Subsystems 

i


4.5 Dielectric Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 

4.6 Mobilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 

4.7 Impact Ionization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 

5 Numerical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 

5.1 High and Zero Frequency AC Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . 43 

5.1.1 General Principle of AC Small Signal Analysis . . . . . . . . . . . . . . . . . . . . . 43 

5.1.2 Matrix Transformation to Improve Diagonal Dominance . . . . . . . . . . . . . 46 

5.1.3 Pre-conditioned TFQMR Method for AC Analysis . . . . . . . . . . . . . . . . . . 47 

5.1.4 Zero Frequency AC Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 

5.2 Discretization Scheme for Carrier and Energy Fluxes . . . . . . . . . . . . . . . 50 

5.3 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 

5.4 Newton Projection Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 

5.5 Global Data Structure in PISCES-2ET . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 

6 Simulation Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 

6.1 Substrate Current of MOS Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 

6.2 SOI Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

6.3 Cylindrically Symmetric LED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 

6.4 AlInAs/GaInAs MODFET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 

APPENDIX A Fermi-Dirac Distribution and Heterostructures . . . . . . 77 

APPENDIX B Mathematical Properties of Fermi Integral. . . . . . . . . . 87 

APPENDIX C Formulations in Previous PISCES-II Versions. . . . . . . 91 

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 

User’s Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 

CHECK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 

COMMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 

CONTACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 

CONTOUR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 

DEEPIMPURITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 

ii 

PISCES-2ET and Its Application Subsystems


DOPING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117 

ELECTRODE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127 

ELIMINATE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130 

END (QUIT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132 

EXTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133 

IMPACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136 

INCLUDE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138 

INTERFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .139 

LOAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141 

LOG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144 

MATERIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146 

MESH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151 

METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157 

MOBILITY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164 

MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .170 

OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180 

PLOT.1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .183 

PLOT.2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .192 

PRINT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .196 

REGION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .200 

REGRID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .206 

SOLVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .212 

SPREAD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .222 

SYMBOLIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .226 

TITLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .230 

VECTOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .231 

X.MESH, Y.MESH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .233 

PART II 

Curve Tracer 

Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .235 

7 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .237 


iii


8 Shell Command Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 

9 Trace File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 

9.1 CONTROL Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 

9.2 FIXED Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 

9.3 OPTION Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 

9.4 SOLVE Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 

10 Input Deck Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 

10.1 Load and Solve Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 

10.2 Contact Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 

10.3 Method Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 

10.4 Options Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 

11 Data Format in Output Files. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 

12 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 

13 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 

13.1 BVCEO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 

13.2 GaAs MESFET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 

Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 

PART III Mixed-Mode Device/Circuit Simulator 

Acknowledgment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 

14 Mixed-Mode Circuit and Device Simulation. . . . . . . . . . . . . . . . . 267 

14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 

14.2 Equations for Circuit Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 

14.3 Equations for Device Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 

14.4 Mixed-Mode Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 

14.5 Computational Cost and Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 

14.6 Parallelization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 

iv 



15 Use of Mixed-Mode Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . .275 

15.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275 

15.2 New SPICE Cards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .275 

SPICE Element Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .276 

SPICE Model Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .279 

15.3 Running a Mixed-Mode Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .286 

15.3.1 Files Required and Generated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 

15.3.2 Method and Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 

15.3.3 Types of Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 

16 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .291 

16.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .291 

16.2 Single Stage CMOS Inverter (DC Analysis) . . . . . . . . . . . . . . . . . . . . . .291 

16.3 High Frequency GaAs MESFET (AC Analysis) . . . . . . . . . . . . . . . . . . .292 

16.4 SRAM Cell (Transient Analysis) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .294 

16.5 GaAs/AlGaAs LED (Transient Analysis). . . . . . . . . . . . . . . . . . . . . . . . .298 

17 System Reconfiguration for a Different Device Simulator . . . . . .303 

17.1 Changes in SPICE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .303 

17.1.1 New Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 

17.1.2 Steps for Adding Numerical Devices to SPICE . . . . . . . . . . . . . . . . . . . . 304 

17.1.3 Increasing Number of Nodes for a SPICE Device . . . . . . . . . . . . . . . . . . 306 

17.1.4 Configuring NPISC for Use with PVM. . . . . . . . . . . . . . . . . . . . . . . . . . . 306 

17.1.5 Different Versions of SPICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 

17.2 Adding Another Device Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311 

17.2.1 Changes to Device Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 

17.2.2 Changes to Mixed-Mode Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .315 


v


vi 


PART I 


for Silicon and Heterostructures 

Zhiping Yu, Datong Chen, Lydia So, 

and Robert W. Dutton

CHAPTER 1 

Introduction and 

Acknowledgment 

PISCES-2ET is a dual energy transport (for carrier temperatures and lattice thermal diffusion) version 

of PISCES-II developed based on Stanford’s 9009 version and Intel’s enhanced 8830 version. This 

work is completed under the support of SRC (Semiconductor Research Corp.), ARO (Army Research 

Office), and ARPA (Advanced Research Projects Agency) and with close collaboration from Intel and 

HP. There are many new features available in the 2ET version, predominately, the capabilities to 

simulate the carrier and lattice temperatures and heterostructures in compound semiconductors. Hence, 

various non-stationary phenomena such as hot carrier effects and velocity overshoot can be analyzed 

using this program. The electrical behavior of optoelectronic devices can also be simulated with 

reasonable accuracy. Most of the material parameters have been calibrated and thoroughly surveyed 

with the help from industry. Other new features which can be found in PISCES-2ET include: 

• High and zero frequency small signal AC analysis 

• Improved initial guess using Newton projection method 

• Carrier energy dependent mobility and impact ionization models 

• About ten different local and non-local (electric) field dependent mobility models 

• Parameterization of array sizes for expansion of maximum grid number 

• ASCII and binary exchange data format with process simulation programs 

PISCES-2ET – 2D Device Simulation for Si and Heterostructures 1

Introduction and Acknowledgment 

This document is organized as follows. CHAPTER 2 discusses the theoretical background for 

DUET transport model, which is based on the moment approach to solving Boltzmann Transport 

Equation (BTE) and is applicable to heterostructure analysis also. In CHAPTER 3, physical models 

used in the program are described. The emphasis is on the various mobility models, many parameters 

of which have been calibrated by industrial users. Material parameters for four common compound 

semiconductors, namely Ge x Si 1-x , Al x Ga 1-x As, Al x In 1-x As, and Ga x In 1-x As y P 1-y , used in 

heterostructure and optoelectronic devices are discussed in CHAPTER 4. Discussion of carrier 

transport in heterostructures and issues related to Fermi-Dirac (FD) statistics are delayed until 

APPENDIX A to provide a complete picture of DUET model yet not to inundate the concise forms in 

the main text with complex coefficients required by using the FD distribution. In CHAPTER 5, 

relevant numerical techniques are presented, including the algorithms for small signal AC analyses. 

Besides, the details in parameterization of global arrays used in the device solver are provided. Finally 

four simulation examples are included in CHAPTER 6. The first two examples compare the simulated 

results to the experimental data regarding the carrier temperature effects in FET structures to establish 

the confidence level of the energy transport model used in the code. The other two examples are about 

the simulation of heterostructures including one application in a realistic, cylindrically symmetric LED 

(light emitting diode) structure. Two short appendices, one dealing with the mathematical properties 

of Fermi integral (APPENDIX B) and the other listing several expressions referred to in this document 

from the previous PISCES reports (APPENDIX C), are included for users’ reference. Finally a user’s 

manual provides the detailed syntax and usage of all commands available in the program. 

Authors are grateful to many contributions from both academia and industry during the 

development of PISECE-2ET. The DUET transport model has been developed in collaboration with 

Prof. K. Hess’ group in University of Illinois at Urbana. One of the key developers, Dr. E. Kan, who 

recently joined our group at Stanford, made numerous contributions to the code including helping 

parameterize the data structure and model calibration. Drs. T. Thurgate of Intel and M. Tan of HP have 

been working closely with us from the very beginning of this project and provided access to their codes 

and experimental data. Various industrial connections under the sponsorship of SRC are greatly 

appreciated, including, but by no means being complete, Drs. R. Lowther of Harris Semiconductor, I. 

Lim of Motorola, and K. L. Chen of OCD in HP. Dr. K. Wu of this group at Stanford developed the 

algorithm for high frequency small signal AC analysis, and Mr. A. Mujtaba helped review the section 

of mobility models. Their contributions are greatly appreciated. Finally, the continuous funding from 

2 PISCES-2ET – 2D Device Simulation for Si and Heterostructures


SRC through contract #SRC 93-SJ-116 is one of the key factors to the success of this program 

development and the grant from ARO through contract DAAL 03-91-G-0152 plays a critical role in 

extending the simulation capabilities from silicon to compound materials and heterostructure. The 

GaAs work was supported through ARPA contract DAAL 01-91-K-0145. Their support are gratefully 

acknowledged. 




CHAPTER 2 

DUET Carrier Transport 

Model 

The DUET model, a carrier transport model in semiconductors, is developed based on the moment 

approach to solving Boltzmann Transport Equation (BTE). It uses six state variables to describe the 

status of a semiconductor device. These six variables are: electrostatic potential, ψ, carrier 

concentrations, n and p, carrier temperatures, T n and T p , and lattice temperature, T L , and they are 

functions of space and time. All other device characteristics such as terminal I-V characteristics and 

circuit model parameters can be calculated from the knowledge of the distribution of these basic 

variables. To determine the distribution of these variables under applied bias, six independent 

equations are required together with proper boundary conditions. It is well established that with the 

drift-diffusion (DD) carrier transport model, Shockley semiconductor equations, i.e., Poisson’s 

equation and carrier continuity equations, govern the distribution of ψ, n, and p. The carrier 

concentrations can also be replaced, equivalently, by their respective quasi-Fermi levels, and , 

in classical distribution (either Boltzmann or Fermi-Dirac) functions. With the temperatures for both 

carriers and lattice introduced as independent variables, three more equations are needed and they can 

be derived from the energy balance principle. In this chapter, we will first introduce two (kinetic) 

energy balance equations for carriers and one thermal diffusion equation for the lattice. Various macro 

quantities such as carrier and energy densities will be defined using the distribution function at the 

quasi-thermal equilibrium. The auxiliary expressions for transport are provided. Finally the proper 

boundary conditions for solving differential equations are discussed. 

φ n 

φ p 


DUET Carrier Transport Model 

2.1 Boltzmann Transport Equation and 

Distribution Function 

The key assumption in the DUET model is that the true distribution function can be constructed based 

on the quasi-thermal equilibrium function using the perturbation theory as follows [1]: 

h 

h ∂ f 

f ( r, 

k) f 0 ( r, 

k) τ( r, 

k) 

------------ k ∇ f (2.1) 

2πm * 0 

------------ 0 

= – ⎛ ⋅ – ------- k ⋅ E⎞ 

⎝ 

2πm * ∂ε ⎠ 

where r and k are spatial (position) and wavenumber vectors, respectively, f 0 is the distribution 

function at the quasi-thermal equilibrium in both the real ( r) and momentum ( k) space, τ is the 

relaxation time which depends on both r and k, and so is defined in a microscopic sense, E is the 

electric field and ε is the carrier kinetic energy, e.g. for electrons, ε = E – E C where E C is the 

conduction band edge. Note that in this manual, we use bold faced E ( E ) and it components to 

represent the electric field, while the plain faced E is used for the total energy of carriers. All other 

symbols in the above expression have conventional meanings. 

f 0 

The quasi-thermal equilibrium function, , is chosen from one of the classical distribution 

functions and for the present we will use the Boltzmann distribution function. In APPENDIX A, we 

will describe how to extend the distribution function to Fermi-Dirac statistics. The Boltzmann 

distribution function has the following form in r and k space: 

⎛ E – E 

f 0 ( r, 

k) 2 exp Fn 

⎞ ⎛ ε – ( E 

⎜–------------------ 

⎟ 2 exp 

Fn – E C ) ⎞ 

= = ⎜–----------------------------------- 

⎟ 

(2.2) 

⎝ k B T n ⎠ ⎝ k B T n ⎠ 

where E Fn and T n are the quasi-Fermi energy and temperature for electrons, respectively. In our later 

analysis, it is often desirable to express f 0 in terms of the carrier concentration. We now proceed this 

transformation. From definition, it is easy to conclude that the carrier concentration is the zeromoment 

of the distribution function in k space. Thus taking electrons as an example, we have 

N C 

⎛ 

n N C exp E Fn – E C ⎞ 

= ⎜--------------------- 

⎟ 

⎝ k B T n ⎠ 

where is the effective density of states for the conduction band and is found to be 

(2.3) 



N C 

⎛ 

2 2πm * n( T L )k B T 

------------------------------------ n ⎞ 3 ⁄ 2 

= ⎜ 

⎟ 

⎝ 

⎠ 

h 2 

where T L is the lattice temperature and because in our DUET model, T L is not necessarily the same 

* 

as T n , we have explicitly indicated the lattice temperature dependence of the effective mass, m n . 

Expressing E Fn – E C in terms of n in Eq. (2.3), we obtain an expression of f 0 as function of n, T n , 

, and ε as follows: 

T L 

(2.4) 

2n ε 

f 0 ( r, 

k) = f 0 ( n( r) , T n ( r) , T L ( r)ε 

, ) = ---------------------------exp⎛–----------- 

⎞ 

N C ( T n , T L ) ⎝ k B T n 

⎠ 

This form of distribution function constitutes the basis for our model discussion. 

(2.5) 

2.2 Energy Balance and Thermal Diffusion 

Equations 

Temperature is a measure of the kinetic energy for random motion and the equation governing the 

carrier/lattice temperature can be derived from the energy balance principle. Because of the free 

particle nature of carriers, Fick’s second law is applied to describe the carrier kinetic energy balance 

(or continuity). For electrons, the continuity principle dictates 

∂w 

-------- n 

= – ∇ ⋅ s (2.6) 

∂t 

n + j n ⋅ E n – u wn 

where w is the kinetic energy density and s is the energy flux, and both can be defined and evaluated 

from the carrier distribution function. The last two terms on the right hand side (RHS) of the above 

equation represent the energy conversion and net loss rates, respectively. The familiar Joule heat term, 

j where is the electric field acting on electrons 1 n ⋅ E n E n , actually represents the rate of conversion 

from the electrostatic potential to the kinetic energy, and u w is the rate of net loss (loss minus 

1. In heterostructures, the electric field acting on carriers is in general different for electrons and 

holes. 



generation) for kinetic energy due to carrier recombination/generation and energy exchange with the 

lattice through phonon scattering. The first step in the development of carrier transport model is then 

to define and determine the expressions for various quantities used in the above balance equation. 

DUET model is based on the Stratton’s description of distribution function at non-thermal equilibrium 

(Eq. (2.1) and refer to [1] for details). The concept of the carrier temperature can directly be deduced 

from the definition of the kinetic energy density in this approach, and it turns out that the parameter 

T c , where c stands for either n or p, used in the distribution function, 

,at quasi-thermal equilibrium 

(Eqs. (2.2) and (2.5)) is the carrier temperature following the ideal gas kinetics. The carrier 

concentration (n), kinetic energy density (w n 

), current density (j n 

), and energy flux (s n 

) can all be 

evaluated from the distribution function, f in Eq. (2.1), from their respective definitions by integration 

in the momentum (i.e. k ) space: 

f 0 

n 

fd 3 ⎛ 

∫ 

p N C exp E Fn – E C ⎞ 

= = ⎜--------------------- 

⎟ 

⎝ k B T n ⎠ 

∫ 

p 2 

w n = --------- fdp3 = 

2m n 

* 

3 

--nk 

2 B T n 

(2.7) 

(2.8) 

j n 

q 

= –----- pfd 3 p 

m n 

* 

∫ 

3 

* 

= qD n ∇n – --qnD 

2 n ∇lnm n + nµ n ∇E C + qnD T n ∇T n 

= nµ n ∇E Fn + qnµ n Q n ∇T n 

(2.9) 

m n 

* 

∫ 

1 

s n = ----- p--------- p2 

fd 3 p = 

2m n 

* 

– P n T n j n – κ n ∇T n 

(2.10) 

where we have introduced the carrier momentum, p = ( h ⁄ 2π)k 

, and the integral element volume, 

d 3 p = ( dk and constant effective mass in (crystal) momentum space is assumed 1 x dk y dk z ) ⁄ ( 2π) 3 

. 

The transport coefficients D (diffusion constant), µ (carrier mobility), D T (thermal diffusivity or called 

“Soret” coefficient in [1]), Q (thermopower), P (thermoelectric power), and κ (thermal conductivity) 

1. This assumption is not required in the DUET model (see [2]) but is used for present implementation 

of the code. 



are all defined and can be evaluated from the even part of the distribution function f in the momentum 

space ( f 0 in Eq. (2.1) for DUET model), and are thus related to each other. For continuity of 

presentation, the expressions for these coefficients are not given here, rather they can be found in 

APPENDIX A. We now consider the rates for energy generation g w and loss r w , from which 

u w = r w – g w 

(2.11) 

r w is related to both carrier recombination and energy transferring from carriers to the lattice. At 

present, three recombination mechanisms are considered in the model and they are Shockley-Reed- 

Hall (SRH), Auger, and radiative recombinations. For g w , only the impact ionization, which is the 

inverse process of Auger recombination, is taken into account 1 . With all relevant mechanisms 

identified, we are able to list the complete set of equations for the DUET model and their auxiliary 

expressions as follows: 

Poisson’s equation: 

+ – 

∇⋅ (– 

ε∇ψ) 

= q( p – n + N D – N A ) 

where dielectric constant, ε , is not to be confused with carrier kinetic energy, ε . 

(2.12) 

Carrier continuity equations: 

∂n 

----- 

∂t 

1 

--∇ ⋅ j 

q n – u 

∂p 1 

----- = –--∇ ⋅ j 

∂t q p – u 

where u is the net recombination rate of electron-hole pairs. 

= 

(2.13) 

(2.14) 

Carrier (kinetic) energy balance equations: 

∂w 

-------- n 

= – ∇ ⋅ s 

∂t 

n + j n ⋅ E n – u wn 

(2.15) 

1. Thus, photo-generation as discussed in Section 3.3.2 applies only to the conservation of carrier 

population. 



∂w 

-------- p 

= – ∇ ⋅ s 

∂t 

p + j p ⋅ E p – u wp 

(2.16) 

Thermal diffusion equation for the lattice: 

c L 

∂T L 

3 

3 

-------- = ∇ ⋅ ( κ 

∂t 

L ∇T L ) + u SRH 

--k 

2 B T n + E g ( T L ) + --k 

2 B T p + 

w n ( T n ) – w n ( T L ) w 

---------------------------------------- p ( T p )– 

w p ( T L ) 

+ ----------------------------------------- 

τ wn 

where and are energy relaxation times for electrons and holes, respectively. 

τ wp 

(2.17) 

τ wn τ wp 

j n qD n ∇n 

The following auxiliary expressions are needed for current and energy flux densities, and 

energy loss rate in Eqs. (2.15)-(2.17). 

Current densities: 

3 

* 

= – --qnD 

2 n ∇lnm n + nµ n ∇E C + qnD T n ∇T n 

= nµ n ∇E Fn + qnµ n Q n ∇T n 

(2.18) 

j p 

= 

= 

3 

* 

– qD p ∇p + --qpD 

2 p ∇lnm p + 

pµ p ∇E Fp – qpµ p Q p ∇T p 

pµ p ∇E V – qpD T p ∇T p 

(2.19) 

Energy flux densities: 

s n 

= 

– P n T n j n – κ n ∇T n 

(2.20) 

s p = P p T p j p – κ p ∇T p 

(2.21) 

where D and µ are related by Einstein relationship (see Eq. (A.23) for a general expression) and Q is 

also linked to µ in a more complex way (Eq. (A.43)), other coefficients have more simple expressions 

if only Boltzmann statistics is considered. 

3 

P n P p P -- k B 

= = = ---- 

2 q 

(2.22) 



κ n 

= 

nk B T n µ n P 

(2.23) 

κ p 

= pk B T p µ p P 

(2.24) 

It is apparent that the carrier mobility, µ, is the key parameter to other transport coefficients, and the 

mobility can be obtained either from the theoretical calculation or more often through empirical or 

semi-empirical formulation by fitting the analysis/simulation results to the experimental data. We will 

discuss in a great detail the mobility modeling in CHAPTER 3. Finally, the rate of net loss of carrier 

kinetic energy is modeled as follows: 

3 

3 

u wn = -- ( u 

2 SRH + u rad )k B T n – ( u n, Auger – g nimp , ) E g ( T L ) + --k 

2 B T p – 

3 

w 

--g k 

2 B T n ( T n ) – w n ( T L ) 

n – ---------------------------------------- 

pimp , 

τ wn 

(2.25) 

3 

3 

u wp = --( u 

2 SRH + u rad )k B T p – ( u p, Auger – g pimp , ) E g ( T L ) + --k 

2 B T n – 

3 

w 

--g k 

2 B T p ( T p )– 

w p ( T L ) 

p – ----------------------------------------- 

nimp , 

τ wp 

(2.26) 

where u SRH , u rad , and u Auger are net carrier loss rates due to SRH, Auger, and radiative 

recombinations, respectively, g imp is the generation rate due to the impact ionization (II). Note that for 

both Auger recombination and II, we need to distinguish if they are caused by electrons or holes. The 

last term on RHS of each above expression represents the energy exchange between the carriers and 

lattice. 

A special case for the above general description (Eqs. (2.15)-(2.17)) is when only the lattice 

temperature is of concern, i.e., the carriers can be considered to have the same temperature as the 

lattice. Such a scenario is often encountered in, say, the simulation of power devices. We can then lump 

Eqs. (2.15)-(2.17) by requiring all temperatures being the same (designated T) and need to solve the 

following thermal diffusion equation only. 

∂ 3 

----- c (2.27) 

∂t L + --( n+ 

p)k ⎝ 

⎛ 2 

B ⎠ 

⎞ T = ∇ ⋅ ( κL ∇T – s – s ) + j n p n ⋅ E n + j p ⋅ E p + u SRH E g ( T ) 

Together with Poisson’s (Eq. (2.12)) and carrier continuity equations (Eqs. (2.13)-(2.14)), these four 

equations are solved for four state variables: ψ, n, p, and T (for both lattice and carriers). 



2.3 Boundary Conditions 

Since the DUET model uses both carrier and lattice temperatures to specify the device state, we also 

need to establish thermal boundary conditions for temperatures in addition to the electrical boundary 

conditions (See [3] and [4] for detailed discussion). We discuss here only the thermal boundary 

conditions. 

Normally the Dirichlet thermal boundary condition, i.e., the known carrier and lattice 

temperatures, is applied to both thermal and electrical contacts. In many cases, however, the heat 

conduction through the intimate contacts to the device is modeled by a thermal resistance. In this case, 

the lattice (and carrier) temperature at the contact becomes unknown. The relationship between the 

heat flux and temperatures at the contact ( 

) is specified as follows: 

T L, 

cont 

) and thermo-reservoir (the environment temperature, 

T env 

F th 

T env T L cont 

– 

= -------------------------------- , 

(2.28) 

R th 

where the direction of the heat flux, F th , is defined as going into the device. In the present model, the 

carrier temperature is always assumed the same as the lattice temperature at the contact. There may be 

two types of contacts to the device: electrical and thermal ones. An electrical contact must be a thermal 

contact also, but the contrary is not necessarily true. For those boundaries of a device region where 

there is no electrical/thermal contact specified, a reflective boundary condition is assumed as is the 

case for electrical boundary conditions. 


CHAPTER 3 

Physical Models 

3.1 Mobility Models 

Carrier mobility is one of the most important parameters in the carrier transport model. In PISCES- 

2ET, the mobility is, for most cases, modeled as the function of the total doping density, N, lattice 

temperature, T L , surface/interface scattering mechanisms which are generally modeled using the 

dependence on the transverse electric field to the surface/interface, and the electric field along the 

current path (longitudinal field). When the device size is in the submicron regime, however, the local, 

longitudinal field dependence may not be accurate enough and non-local effects, which is mainly 

characterized by the carrier temperature dependence, have to be taken into consideration. The 

following expression describes in a general way the carrier mobility dependence on various factors: 

µ ( N, T L , E ⊥ , E || /T c ) = f ( µ 0 ( N, T L , E ⊥ ), 

E || /T c ) 

(3.1) 

where E || and E ⊥ are the longitudinal and transverse components of the electric field with respect to 

(w.r.t) the current direction, µ 0 

, which depends on N, T L 

, and E ⊥ , is called the low field mobility 

because when E || → 0 , µ → µ 0 , T c 

is the carrier temperature with the subscript c representing either 

n or p for electrons and holes, respectively, and the symbol E || ⁄ T c indicates the dependency is either 

on E || or on T c but not on both. In some models such as ones developed by Intel, the above expression 

is simplified to the following form to separate mobility reductions due to different field components: 



µ ( N, T L , E ⊥ , E || /T c ) = µ 0 ( N, 

T L ) ⋅ r perp ( E ⊥ ) ⋅ r para ( E || ) 

(3.2) 

where r’s are reduction factors and the subscripts perp and para represent the perpendicular and 

parallel components of the electric field. 

In the following, we will first consider the low field mobility models without taking into account the 

effect of E ⊥ . We then consider the effect of the transverse field dependence and finally discuss the 

longitudinal field or carrier-temperature dependence. 

3.1.1 Low field Mobility Models 

Without considering the transverse field dependence, the low field mobility can be written as µ 0 

(N, 

T L 

). There are six such models available in PISCES-2ET. 

3.1.1.1 Constant Mobility 

This mobility model is invoked when none of the following logical parameters is included in the 

model card: conmob, ccsmob, analytic, arora, and user1. The mobility is then the function 

of material only and does not dependent on the doping density. However, the field dependency can still 

be included in the simulation when other parameters such as fldmob (for longitudinal) and tfldmob 

(for non-local transverse field) are specified in the model card. The values for four group of 

semiconductor materials are listed in TABLE 3.1. 

TABLE 3.1 

µ n (cm 2 V -1 s -1 ) µ p (cm 2 V -1 s -1 ) 

Silicon / Ge x Si 1-x 1500 450 

GaAs / Al x Ga 1-x As 8500 400 

InAs / Al x In 1-x As 22600 250 

InP / Ga x In 1-x As y P 1-y 4500 150 

3.1.1.2 Table Look-up Doping Dependent Mobility 

When the parameter conmob is specified in the model card, the doping dependent mobility model is 

invoked. The default doping dependent model is based on a table look-up of data for silicon if none of 

parameters ccsmob, analytic, arora, and user1 is specified together with conmob in the 

model card(s). Tables of data for other materials are not available at present and constant value will 



be used instead with this option. The range of the data for doping concentrations in silicon is from 

14 

21 

N = 1×10 

to 1×10 cm – 3 . If the doping concentration falls out of the above range then the closest 

boundary value for the mobility is used, otherwise the following interpolation scheme is applied. 

µ 0 ( N 2 )– 

µ 0 ( N 1 ) N 

µ 0 ( N ) = µ 0 ( N 1 ) + ---------------------------------------- log------ 

(3.3) 

log( N 2 ⁄ N 1 ) N 1 

where N 2 > N > N 1 . This model is valid for silicon only. Note that if any of the following parameters: 

ccsmob, analytic, arora, and user1, is used with or without conmob specified in the model 

card, that model takes precedence and the precedency of these models is user1, arora, analytic, 

and ccsmob with each preceding one overriding the trailing ones. 

3.1.1.3 Analytical Doping Dependent Mobility Model 

This model is invoked by parameter analytic in the model card. The formulation for this model 

is as follows: 

µ 0 ( N, 

T L ) = γµ surf ( N, 

T L ) + ( 1 – γ )µ bulk ( N, 

T L ) 

(3.4) 

where γ is a coefficient with value between 0 and 1 depending on the relative distance from the surface/ 

interface, µ surf 

and µ bulk 

are mobilities in the surface layer and bulk, respectively. γ is determined by 

an ERFC function as follows: 

γ 0.5 erfc y – y int – d 

= ⋅ ⎛------------------------- 

⎞ 

(3.5) 

⎝ λ ⎠ 

where the silicon and SiO 2 interface is assumed to be parallel to the x-axis, is the y coordinate of 

the interface, d and λ are two parameters: one for offset and the other for the characteristic length. 

Their default values are d = 0.06µ and λ = 0.03µ , and both can be accessed by users via parameters 

int.off and char.int in mobility card, respectively. 

The surface and bulk mobilities have the same form of dependence on N and T L 

as follows: 

y int 

µ ( N, 

T L ) 

T L 

d 

---------------------- 1 + α( N ) 

µ α ( N ) 

= 

+ ---------------------- max 1 + α( N ) 

µ min 

(3.6) 



where α( N ) ( N ⁄ N 0 ) c b 

= T L and hereinafter T L = T L (in K) ⁄ 300, the normalized lattice 

temperature. But N has different meaning for bulk and surface. For bulk, N is simply the total doping 

concentration, while for surface N must include the effect of the interface charge in the following 

manner: 

N = N + cQ int 

(3.7) 

where Q is interface charge (in units of cm -2 int ) as specified by parameter qf in the interface card, 

and c is a scaling factor in units of cm -1 with default value of 10 7 and can be changed through 

parameter qss.conc in mobility card. Note that the effect of the surface mobility is taken into 

account only for those nodes which are directly (in the y-direction) under the Si/SiO 2 interface. There 

is one exception, however. That is, when the flag intelmob.par is set in model card, the surface 

mobility ( µ srf in Eq. (3.4)) uses a different expression from Eq. (3.6). The new expression has the form 

of 

– a 

µ srf = µ 0 T L 

where parameters and a for silicon are listed in Table 3.2. 

(3.8) 

µ 0 

Table 3.2 

µ (cm 2 V -1 s -1 0 ) a 

electrons 783.5 1.67 

holes 247.4 1.13 

µ max µ min N 0 

There are six parameters in Eq. (3.6): , , , b, c, and d, and all are dependent upon 

the carrier type (electrons or holes) and region (bulk or surface). The parameter values used in the code 

for silicon are listed in Table 3.3. 

Table 3.3 

electrons 

holes 

µ max (cm 2 V -1 s -1 ) µ min (cm 2 V -1 s -1 ) N 0 (cm -3 ) b c d 

bulk 1400 55.24 1.1 × 10 17 -3.8 0.73 -2.3 

surface 1200 1200 1.1 × 10 17 -3.8 0.73 -2.3 

bulk 500 49.7 1.6 × 10 17 -3.7 0.70 -2.2 

surface 500 49.7 1.6 × 10 17 -3.7 0.70 -2.2 



3.1.1.4 Arora’s Doping and Temperature Dependent Mobility Model 

An empirical mobility model based on the fitting to the measurement data for silicon at different lattice 

temperature has originally been proposed by Arora and et al. [5] and can be invoked by using 

parameter arora in the model card. The model has a general form of the following: 

µ 0 

µ 

( N, 

T L ) = µ min + -------------------------------- dlt 

1 + ( N ⁄ N 0 ) α 

(3.9) 

† units of cm 2 V -1 s -1 b 

where parameters µ min , µ dlt , N 0 

, and α are all functions of T L 

in the form of aT L where both a and b 

are constants. This model is later extended to apply to GaAs by Yu [6] based on the available measured 

data at 77 and 300 K. The parameter values for silicon and GaAs are listed in Table 3.4. 

Table 3.4 

† 

µ min 

† 

µ dlt N 0 (cm -3 ) 

α 

electrons 

– 0.57 

88T L 

– 2.33 

1252T L 

17 2.4 

1.25×10 T L 

– 0.146 

0.88T L 

– 0.57 

– 2.23 

17 2.4 

– 0.146 

silicon holes 54.3T L 407T L 2.35×10 T L 0.88T L 

electrons 

– 0.7475 

2136T L 

– 2.687 

6331T L 

16 3.535 

7.345×10 T L 

– 0.1441 

0.6273T L 

– 1.124 

– 2.366 

GaAs holes 21.48T L 331.2T L 

17 3.690 

5.136×10 T L 0.8057 

3.1.1.5 User Definable Arora’s Mobility Model 

This model uses exactly the same formulation for doping and (lattice) temperature dependent mobility 

as Arora’s model discussed above. The only difference is that all the coefficients are put in an 

initializable subroutine initum1 in file usrmob1.f. If users want to change some of the 

coefficients in the model, they have to change this file and re-compile the program. This model can be 

invoked by parameter user1 in model card and is applied to silicon only. 



3.1.1.6 “Carrier-Carrier Scattering” Mobility Model 

Invoked by parameter ccsmob in model card, the so-called “carrier-carrier scattering” mobility 

model follows the approach of Dorkel and Leturcq [7]. The model formulation is as follows and the 

mobility depends on the carrier concentrations also (the name of “carrier-carrier scattering”). 

µ ( N, T L , n, 

p) = µ L ( T L ) 

1.025 

----------------------------------------------------------------------------- – 0.025 

1 + {( X( N, T L , n, 

p) 

) ⁄ 1.68} 1.43 

– α 

µ L ( T L ) = µ L0 T L 

(3.10) 

(3.11) 

X( N, T L , n, 

p) 

= 

6µ L [ µ I ( N, 

T L ) + µ ccs ( T L , n, 

p) 

] 

------------------------------------------------------------------------------ 

µ I ( N, 

T L )µ ccs ( T L , n, 

p) 

(3.12) 

µ I ( N, 

T L ) 

= 

3⁄ 

2 

AT L 

2 

2 

-------------- N 

ln ⎛ 1 BT 

+ --------- L ⎞ BT 

– -------------------- L 

⎝ N ⎠ 

2 

N + BT L 

–1 

(3.13) 

17 

3⁄ 

2 

2×10 T L 8 

µ ccs ( T L , n, 

p) 

= --------------------------- [ ln{ 1 + 8.28×10 T 2 L ( pn) – 1 ⁄ 3 }] – 1 

pn 

where the parameters µ L0 , α , A, and B are listed in Table 3.5. 

(3.14) 

Table 3.5 

µ (cm 2 V -1 s -1 L0 ) α A (cm -1 s -1 V -1 K -3/2 ) B (cm -3 K -2 ) 

electrons 1500 2.2 

holes 450 2.2 

Note that in the program, N is taken as the min (N, 10 19 ) where N is in units of cm -3 . 

3.1.2 Mobility Reduction due to Transverse Field 

4.61×10 1.52×10 

We now consider the effects of the electric field on the mobility. There are two modeling approaches: 

a general one as in Eq. (3.1) in which the effects of the transverse and longitudinal field components 

can be counted for separately, and a more specific form of Eq. (3.2) in which the field effects can be 

factorized. We first discuss the second approach in this section for the reason of simplicity. There are 

17 

17 

1×10 6.25×10 

15 

14 



two such models available in the program, both were developed by Intel (intelmob and 

intelmob.par in model card). We then consider the Lombardi model (lombardi) which shares 

the same feature as Intel’s ones in that both transverse and longitudinal field effects are considered 

simultaneously in the code. In all these three models, the transverse field can be computed either based 

on the structure or by definition. We will elaborate this at the end of this section. 

3.1.2.1 Intel’s Local Field Models 

There are two mobility models developed by Intel for all doping, lattice temperature, and field 

(including both transverse and longitudinal) dependence with one single logical flag. They are 

described in this section. Both models follow the same formulation of Eq. (3.2), and µ 0 ( N, 

T L ) has 

the same expression as Eq. (3.4), the analytical model. 

For model invoked by parameter intelmob in model card, 

r perp = ( 1 + E ⊥ ⁄ E crit ) – β 

(3.15) 

where E crit is a parameter with value of 4.2×10 4 V/cm for electrons and 3×10 4 V/cm for holes in 

silicon, and β = 0.5 . These parameters are all accessible to users through mobility card. 

The second model specified by intelmob.par has different expression for (Eq. (3.8)) 

and more user-accessible parameters for the reduction due to the transverse field: 

µ srf 

1 

r perp = --------------------------------------- 

1 + ( E ⊥ ⁄ E univ ) α 

where the parameters α and E univ 

are listed in Table 3.6. 

(3.16) 

Table 3.6 

electrons 

holes 

α 

E univ ( V/cm) 

1.02 5.71×10 

0.95 2.57×10 

5 

5 

Both Intel’s mobility models use µ 0 ( N, T L , E ⊥ ) = r perp ( E ⊥ )µ 0 

( N, 

T L ) for the low-field mobility. 



3.1.2.2 Lombardi’s Model 

Different from the above approaches of simply applying a reduction factor to the low field mobility, 

PISCES-2ET also provides a more physics based model to account for the effect of the transverse field. 

This model is developed based on extensive experimental data by Lombardi et al. [8] and can be 

invoked by parameter lombardi in model card. This transverse field dependent mobility is 

expressed by using Mathiessen’s rule: 

1 

------------------------------- = 

µ ( N, T L , E ⊥ ) 

1 

1 

------------------------------------ 

(3.17) 

µ ac ( N, T L , E ⊥ ) 

+ 1 

-------------------- 

µ srf ( E ⊥ ) 

+ µ ------------------------ 

0 ( N, 

T L ) 

where µ ac 

is the mobility due to the acoustic phonon scattering, which depends on both the transverse 

field and lattice temperature, µ srf 

is the one due to the surface scattering and is the function of the 

transverse field only, and µ 0 

(N, T L 

) can use any model in Section 3.1.1. The expressions for µ ac 

and 

µ srf 

are as follows 

µ ac ( N, T L , E ⊥ ) 

= 

B 

------ 

E ⊥ 

αN β 

+ ----------------- 

1 ⁄ 3 

T L E ⊥ 

(3.18) 

µ srf ( E ⊥ ) 

= 

δ 

------ 

2 

E ⊥ 

(3.19) 

The parameters used in the above expressions are listed in Table 3.7 for electrons and holes, 

respectively. 

Table 3.7 

electrons 

holes 

B α β δ 

7 

5 

4.75×10 1.74×10 0.125 5.82×10 

7 

5 

9.93×10 8.84×10 0.0317 2.05×10 

14 

14 

Note that the units for N, T L 

and E ⊥ in the above two equations and in conjunction with the use of 

parameter values in Table 3.7 are cm -3 , K, and V/cm, respectively. 



There are now problems remain unspecified in the above Intel’s and Lombardi models. That 

is the evaluation of the transverse field and the reduction due to the longitudinal field. We discuss these 

issues in the following subsections. 

3.1.2.3 Evaluation of Transverse Electric Field 

The transverse field is defined as the field component the direction of which is perpendicular to the 

current flow, so, mathematically 

E × j 

E ⊥ = --------------- 

(3.20) 

j 

PISCES-2ET uses this formula to evaluate E ⊥ in the above three mobility models if the parameter 

strfld is not specified in model card. Such evaluation is computationally costly and might also 

cause numerically instability. Another alternative and simplification is to evaluate the normal field 

component based on the geometric proximity to the Si/SiO 2 interface. Thus when strfld is 

specified, the following formula is used: 

E ⊥ E y e y y int 

= 

(3.21) 

where y is the coordinate in the axis perpendicular to the interface, E y is the transverse field at the 

interface (y int 

), and L is the characteristic length which has a value of 0.5µ. 

3.1.2.4 Watt’s Surface Mobility Model 

–( – ) ⁄ L 

J. Watt of Stanford proposed a simple approach to modeling the surface mobility in the inversion layer 

in silicon near the Si-SiO 2 interface [9]. The inversion layer is assumed to be confined only in the first 

grid spacing in the silicon at the direction perpendicular to the interface. Thus the interface is at the top 

of the inversion layer whereas the first grid in the silicon lies at the bottom of the inversion layer. The 

requirement for the meshing when this model is to apply is that the top grid spacing should be 

reasonably large (a couple of hundred angstroms), quite contrary to the conventional thought that the 

meshing should be dense at the substrate surface. The carrier mobility in the inversion layer, µ 0, 

inv , 

depends on the effective transverse field, E ⊥, 

eff , in the inversion layer. The model accuracy has been 

verified against the measurement and is in agreement with the universal mobility model requirement 

[10]. This model can be invoked by using parameter srfmob in the model card. The effective 

transverse field, , is defined and calculated as: 

E ⊥, 

eff 



1 

E ⊥, eff = 

ε si 

----- ( ζQ d + ηQ i ) 

(3.22) 

where Q d is the charge density (per unit surface area) in the inversion layer due to the ionized 

impurities and Q i is the charge density due to the inverted (minority) carriers, and both ζ and η are 

physics-based fitting parameters. It is usually taken that ζ = 1 for both carriers and η = 0.5 for 

electrons and η = 0.33 for holes. The dependence of the mobility on E ⊥, 

eff is modeled in the 

following way by using Mathiessen’s rule: 

1 

------------ 

µ 0, 

inv 

1 

= ------- 

µ ph 

1 

= 

1 1 

+ ------ + ------- 

µ sr µ im 

----------- ⎛ 1 6 

------------- 

×10 ⎞ α1 1 

µ ref 1 

⎝E ⊥, 

eff 

⎠ µ ----------- 1 6 

+ ⎛------------- 

×10 

ref 2 

⎝ ⎠ 

1 

µ ----------- ⎛ 1 18 

---------------- 

×10 ⎞ – 1 12 

⎛1×10 

---------------- ⎞ α3 

+ 

ref 3 

⎝ N B 

⎠ ⎝ N i 

⎠ 

⎞ α2 

E ⊥, 

eff 

(3.23) 

where µ ph 

is the mobility due to the phonon scattering, µ sr 

is the one due to the surface roughness 

scattering, and µ im 

is due to the scattering of the charged impurities in the inversion layer. And N B 

is 

the doping density in the substrate (units of cm -3 ), and N i 

is the inverted carrier density per unit surface 

area in the channel (units of cm -2 ). The other parameters are listed in Table 3.8. 

Table 3.8 

η µ ref 1 α1 µ ref 2 α2 µ ref 3 α3 

electrons (295K) 0.50 481 -0.160 591 -2.17 1270 1.07 

electrons (77K) 0.75 5260 0.334 1700 -2.32 680 1.03 

holes (295K) 0.33 92.8 -0.296 124 -1.62 534 1.02 

holes (77K) 0.45 280 -0.516 213 -1.86 210 1.03 

The modeling of mobility dependence on the transverse field can generally be categorized as 

two classes: local or non-local field dependence. The local field dependence refers to the fact that the 

transverse electric field is computed locally, whereas non-local field dependence is to find an effective 

transverse field to be used in the mobility formulation and this effective field is computed based on the 

knowledge over the entire inversion (or accumulation) layer in the silicon substrate at the Si/SiO 2 



interface. All the models discussed so far are of local field nature. In next section we will discuss two 

non-local models, both developed at University of Texas, Austin. 

3.1.2.5 Shin’s Non-local Transverse Field Models 

A non-local mobility model is the one in which the mobility is not solely determined by the local 

electric field and there are some non-local quantities in the mobility formulation. For example, the 

mobility in the inversion layer at the surface of the substrate below the gate oxide may also be affected 

by the inversion layer conditions (layer thickness, etc.). In the following, we first provide the model 

formulation and then state briefly the requirement on the user input. The first model, invoked by 

parameter oldtfld in model card has the following dependence [11]: 

µ ( N, T L , E ⊥ , E || ) 

= 

µ 0 ( N, T L , E ⊥ ) E ⊥ – E 

--------------------------------- --------------------------------------- dµ 0 0 

+ 

--------- 

µ 0 E || 

1 + ----------- 

⎝ 

⎛ µ 0 E || 

⎠ 

⎞2 1 + ----------- 

⎝ 

⎛ ⎠ 

⎞2 

3 ⁄ 2dE ⊥ 

v sat 

v sat 

(3.24) 

where the dependence of µ 0 is listed only once. Note that all four parameters, N, T L , E ⊥ , and E || are 

functions of space, so are µ and µ 0 . The non-locality is represented by the quantity of E 0 which is 

defined as the transverse electric field at the edge (i.e. bottom) of the inversion layer. The inversion 

layer edge is in turn determined by the criterion that the inverted carrier concentration starts to drop 

below the doping density. The expression for is 

µ 0 

where 

µ 0 ( N, T L , E ⊥ ) 

= 

⎛ ------------------------ 1 

3.2 –9 

×10 --T p 1 ⁄ 2 

+ 

⎞ – 1 

⎝ – 5 ⁄ 2 

1150T 

z L 

⎠ 

L 

(3.25) 

3 ⁄ 2 

p = 0.09T L + 1.5×10 

–8 

N f 

---------------- 

n 1 ⁄ 4 T L 

(3.26) 

0.039T 

z 

L 1.24×10 

= ------------------- + ------------------------------ 

E ⊥ + E 

------------------ 0 ⎛ 

E ⊥ + E 

------------------ 0 ⎞ 1 ⁄ 3 

2 ⎝ 

2 

⎠ 

(3.27) 

where n is the inverted carrier density in the inversion layer and in this particular case is the electron 

concentration for the n-channel MOSFET, and N f is the fixed interface charge per unit area at the Si/ 

–5 



SiO 2 interface. To use this model, users need to provide the location of the gate oxide through 

parameters ox.left, ox.right, and ox.bottom in the model card. 

An extended version of Schwarz-Russek formulation [12] is also available in the code by 

specifying tfldmob in the model card. The formulation and its parameters are described below: 

µ 0 ( N, T L , E ⊥ ) 

1 1 1 

= ⎛------- 

+ ------ + ----- ⎞ 

⎝ 

⎠ 

(3.28) 

where µ ph 

is the mobility due to the scattering by phonons in both bulk and surface and fixed interface 

charge, and µ sr 

is the one due to the surface roughness scattering, and µ C 

is to the screened Coulomb 

scattering. The detailed expressions for those three mobilities can be found in [13]. 

3.1.3 Mobility Dependency on Longitudinal Field/Carrier 

Temperature 

When the electric field along the current flow (called longitudinal field) becomes large, the carrier 

mobility is reduced. This reduction is on top of the reduction due to the transverse field which usually 

happens only at the semiconductor and insulator interface. The longitudinal field reduction of the 

mobility can be modeled either as the function of the local field if the field intensity is not very large 

or the spatial change of either the field or the doping concentration is not very rapid, or as the function 

of the carrier temperature if the energy relaxation process lags apparently behind that of the momentum 

relaxation, a phenomenon termed as the non-local effect. In the following, we first give a general 

formulation for the mobility reduction due to the longitudinal field. Then two models for GaAs are 

provided. One exhibits the behavior of the negative differential mobility when the field exceeds a 

critical value and is the accurate model for electrons in the bulk material. The other has a saturation 

velocity and is suitable for the surface channel mobility modeling. Finally we present two carriertemperature 

dependent mobility models. 

3.1.3.1 General Formulation for Field Dependent Mobility in Silicon 

µ ph 

A general approach to modeling the effect of the longitudinal field on the carrier mobility is to multiply 

a reduction factor with the low-field mobility which may have taken into consideration the effect of 

the transverse field. Thus, 

µ sr 

µ C 

–1 



µ ( N, T L , E ⊥ , E || ) = r para ( E || )µ 0 

( N, T L , E ⊥ ) 

and the reduction factor is modeled as (refer to [14]) 

r para 

(3.29) 

(3.30) 

where in silicon β is 1.395 for electrons and 1.215 for holes, and the saturation velocity, v sat , has the 

expression in Table 3.9. The parameter β can be changed by the user through two parameters, 

b.electrons and b.holes, in the model card. 

3.1.3.2 GaAs Mobility Models 

µ 0 ( N, T L , E ⊥ )E || 

r para = 1 + --------------------------------------- 

⎝ 

⎛ ⎠ 

⎞β 

v sat 

It can be deduced from Eqs. (3.29)-(3.30) that the carrier drift velocity, which is equal to , 

increases monotonically as E || increase and saturates at v sat . However, for electrons in the bulk GaAs 

due to the existence of several valleys with different effective mass in the conduction band structure, 

the drift velocity reaches a peak as the electric field is increased to a critical value and then the velocity 

decreases as the field further increases. This phenomenon, if viewed from the mobility modeling point 

of view, amounts to a negative differential mobility (defined as dv ⁄ dE || ). To model this field 

dependence for electrons in GaAs, a model proposed first by Thim [15] is used as follows: 

– 1 ⁄ β 

µE || 

µ ( N, T L , E || ) 

= 

v sat 

µ 0 ( N, 

T L ) ------- E || 

+ ⎛----- 

⎞ 4 

E ⎝E 0 

⎠ 

----------------------------------------------------- 

E || 

1 + ----- 

⎝ 

⎛ ⎠ 

⎞4 

E 0 

(3.31) 

where E 0 

is the critical field and has a default value of 4kV/cm, and v sat = 1.13×10 – 1.2×10 T L . It 

can be shown that when E > E 0 Eq. (3.31) leads to a negative differential mobility (NDM). This is the 

default field dependent mobility model for electrons in GaAs and the value of E 0 

can be altered by the 

user through the parameter E0 in the model card. 

One problem related to the above formulation is that when applied to the simulation of GaAs 

MESFET, the drain output characteristics (current vs. voltage) may exhibit an unrealistic zig-zag 

behavior. One possible reason is that the correct mobility model in the bulk may not be suitable to the 

carriers in the surface channel. In the program, we provide another mobility model for electrons in 

GaAs, in which the carrier velocity approaches the saturation velocity with increased field 

7 

4 



monotonically in a manner of the hyperbolic tangent function. The model formulation is as follows 

[16] and does not exhibit NDM behavior. 

µ ( N, T L , E || ) 

= 

v sat ⎛µ ------- 0 ( N, 

T L )E || ⎞ 

tanh⎜------------------------------ 

⎟ 

E || ⎝ 

⎠ 

v sat 

(3.32) 

This model can be invoked through parameter hypertang in the model card. 

3.1.3.3 Carrier Temperature Dependent Mobility in Si (Haensch’s Model) 

A carrier temperature instead of local-field dependent mobility model as proposed Haensch [17] is 

available in the program. The normal mobility dependences on doping, lattice-temperature, and 

vertical electric field in the Si-SiO 2 

interface are all preserved in this model. The complete formulation 

for this mobility model as applied to silicon is as follows: 

µ ( N, T L , E ⊥ , T c ) 

µ 0 ( N, T L , E ⊥ ) 

= -------------------------------------------------------------------------- 

3 

1 + --α ( N, T 

2 L , E ⊥ )k B ( T c – T L ) 

(3.33) 

where the subscript c stands for carriers, α is defined as being proportional to µ 0 

in the following way: 

µ 

α( N, T L , E ⊥ ) 0 ( N, T L , E ⊥ ) 

= --------------------------------- 

(3.34) 

2 

qτ w v sat ( T L ) 

where τ w 

is the energy relaxation time and v sat 

is the saturation velocity for carriers, respectively. Their 

default values for silicon are listed in Table 3.9 where is in units K. 

T L 

Table 3.9 

τ w ( ps) v sat ( cm/s) 

electrons 0.42 

holes 0.25 

6 

8.64×10 – 2.68×10 T L 

6 

10.65×10 – 2.68×10 T L 

3 

3 



3.1.3.4 Local Field Dependent Mobility Transformed from Haensch’s Model 

The following mobility model preserves the local field dependency, but it is transformed from 

Haensch’s formulation (Eqs. (3.33)-(3.34)). The model is valid for silicon only and can be invoked 

through parameter fmob.new in model card. 

2 

µ ( N, T L , E ⊥ , E|| 

) = µ 0 

( N, T L , E ⊥ )------------------------------------------------------------------------- 

1 1 4 µ 0( N , T L, 

E ⊥)E --------------------------------------- 2 || 

+ + 

v sat 

(3.35) 

3.2 Thermal Conductivity Formula 

The thermal conductivity, κ, in the expression of carrier-energy/heat flux plays equally important role 

as mobility does in the current density expression. In CHAPTER 2 we have given expressions of κ for 

carriers in terms of the mobility. For thermal conductivity of the lattice, κ L 

, it is assumed that the power 

dependence on the lattice temperature is observed, i.e., 

κ L ( T L ) 

– α 

= κ 0 T L (3.36) 

where κ 0 

is the thermal conductivity at T L 

= 300 K and varies from material to material while α is a 

constant (1.2) for all materials. Table 3.10 lists κ L 

for different materials as implemented in the code. 

Table 3.10 

material κ (W K -1 cm -1 0 ) material κ (W K -1 cm -1 0 

) 

silicon 1.45 oxide 0.25 

GaAs 0.44 nitride 0.25 

AlAs 0.91 sapphire 0.25 

InAs 0.29 insulator 0.25 

InP 0.80 Al 0.5 Ga 0.5 As 0.0903 



3.3 Recombination and Generation Mechanisms 

3.3.1 Impact Ionization Models 

The generation rate of electron-hole pairs due to the carrier impact ionization (II) is generally modeled 

as [18] 1 G = α n nv n + α p pv p 

(3.37) 

where v n 

and v p 

are the electron and hole velocities, respectively, and the impact ionization rates, α n 

and α p 

, which are defined as the number of electron-hole pairs generated by a carrier per unit distance 

traveled. The II rate thus defined is a strong function of the local electric field or more accurately (as 

most researchers now agree) of local carrier temperature. PISCES-2ET provides several II rate models 

having either local field or carrier temperature dependence. In the following we will first discuss the 

more classical local field dependent model and provide the relevant material parameters and then the 

carrier temperature dependent models. 

3.3.1.1 Local Field Dependent II Rate 

–( ⁄ ) 

α Ae b E || 

= 

(3.38) 

where E is the electric field component which is parallel to the current flow, i.e., 

2 || E || = j ⋅ E⁄ 

j . 

The parameters used in the above expression for different materials are listed in Table 3.11 

Table 3.11 

Parameter Si GaAs/Al x Ga 1-x As Ga x In 1-x As y P 1-y Al x In 1-x As 

6 

6 

A n (cm -1 ) 3.8×10 [18] 4.0×10 [19] 3×10 [20] 8.6×10 

[21] 

6 

6 

A p (cm -1 ) 2.25×10 [18] 1.34×10 [18] 3×10 2.3×10 

[21] 

6 

6 

b n (V/cm) 1.75×10 [18] 2.3×10 [19] 6.4×10 [20] 3.5×10 

[21] 

4 

4 

5 

6 

7 

6 

1. Correction has been made to the original formulation (Eq. (80) on p. 59 of [18]). 

2. We do not consider in Eq. (3.38) the situation of j ⋅ E < 0, i.e. the current is against the field direction. 



Table 3.11 

Parameter Si GaAs/Al x Ga 1-x As Ga x In 1-x As y P 1-y Al x In 1-x As 

6 

6 

b p (V/cm) 3.26×10 [18] 2.03×10 [18] 6.4×10 4.5×10 

[21] 

E eff E || 

m n 1 [18] 1 [19] 1 [20] 1 [21] 

m p 1 [18] 1 a 1 1 [21] 

a. 2 in [18] but by comparison to the experimental data 1 is more proper. 

3.3.1.2 Carrier Temperature Dependent II Models 

There are several ways to model the carrier temperature dependent impact ionization. One way is to 

map the carrier temperature to an effective electric field, , in replacing in Eq. (3.38) and all the 

material parameters in the expression are kept unchanged. The mapping between T c 

and E eff is done 

through the following formulation (refer to [22]): 

E eff = 

5 

-- k B 

---- T c – T 

----------------- L 

2 q γ L w 

(3.39) 

where L w = τ w v sat is called the energy relaxation length and γ is an adjustable parameter (for fitting 

the experimental data) which can be accessed by the user using impjt.ratio in the model card 

(default: 1.0). The second way is to approximate the actual carrier (drift) velocity with their saturation 

velocity and to use carrier-temperature dependent ionization rate as follows: 

5 

6 

G 

= 

α( T n )nv sat, n + α( T p )pv sat, 

p 

(3.40) 

– ⁄ B c 

α( T c ) A c e T c 

= 

(3.41) 

where c stands for either n or p. The values of A and B are listed inTable 3.12. This model can be 

Table 3.12 

electrons 

holes 

A (cm -1 ) B (K) 

6 

3.8×10 1.75×10 

7 

2.25×10 3.26×10 

6 

6 

invoked through parameter imp.nvt in the model card. 



The third modeling approach in developing carrier temperature dependent II is to abandon the 

generation rate dependence on the carrier (average) velocity at all. The rationing behind this approach 

is that when the carrier energy is higher than some threshold value the generation rate should be 

determined by the number of high energy carriers only no matter which direction they travel. This 

model can be invoked by parameter imp.nt in the model card, and the formulation and its 

parameters are as follows: 

B 

G nA n T 

n 

n e C n T n 

B 

pA p T 

p 

p e C p 

= 

+ 

where the parameters A, B, and C are listed Table 3.13 

– 

⁄ 

– 

⁄ T p 

(3.42) 

3.3.2 Photo-Generation 

This model is invoked by parameter photogen in the model card. The generation rate due to 

photons is modeled as a forced generation term which is proportional to the photon flux, 

3.3.3 SRH Recombination 

Table 3.13 

A B C 

electrons 5.5×10 

4.0 0.8 

holes 2.0×10 

4.0 1.0 

Shockley-Read-Hall (SRH) recombination rate is determined by the following formula: 

11 

13 

F ph 

, and the 

intensity decays exponentially deep into the device along the incident path. The decay length is 

characterized by the absorption coefficient, α. The current implementation assumes only y- 

dependence: 

gy ( ) = αF ph e – αy 

(3.43) 

where F ph 

has units of cm -2 s -1 and α units of cm -1 . Both F ph 

and α have to be specified by the user 

through parameters flux and abs.coef in the model card. 

2 

np – n 

r i 

SRH = ------------------------------------------------------------------------------------------------------------------------ 

( 

τ n p n i e E i – E t ) ⁄ ( k B T L ) 

( 

[ + 

] τ p n n i e E t – E i ) ⁄ ( k B T L ) 

+ [ + 

] 

(3.44) 



where E t 

is the energy level for the recombination centers and E i 

is the intrinsic Fermi Energy. Carrier 

lifetimes, τ n 

and τ p 

, can be either constant or dependent upon the total doping concentration (parameter 

consrh in model card). The formula for the doping dependent is as follows: 

τ = ----------------------------------- 

(3.45) 

1 + N tot ⁄ N SRH 

where N tot 

is the total doping concentration, and the default values for parameters τ 0 

and N srh 

are the 

–7 

16 

same for both types of carriers in silicon and τ s and cm -3 0 = 1×10 

N srh = 5×10 

. If the interfacial 

recombination is to be included, it is through the change of carrier lifetime in the following way: 

τ eff 

(3.46) 

where A and d are partial area and interface length associated with the node in the element, 

respectively, and is the interface recombination velocity. 

s int 

3.3.4 Auger Recombination 

1 

------- = 

τ 0 

ds int 1 

---------- + -- 

A τ 

This is a three-carrier recombination process, involving either two electrons and one hole or two holes 

and one electron. The dependence on n and p is as follows: 

2 

u Aug ( n, 

p) = ( c n n + c p p) ( np – n i ) 

(3.47) 

–31 

–32 

where the default values for c and in silicon are and cm 6 s -1 n c p 2.8×10 9.9×10 

, respectively. 




CHAPTER 4 

Material Properties for 

Heterostructures 

In CHAPTER 2 and APPENDIX A, expressions are introduced for carrier transport in 

heterostructures. In order to perform the simulation, essential material parameters must be known. In 

this chapter, we will mainly discuss various material properties needed for device simulation and their 

dependence on the composition. 

4.1 Material Parameters for Device Simulation 

Material parameters in compound semiconductors depend strongly on the composition as well as (to a 

lesser degree) on the doping level. We start with identifying which material properties (parameters) 

are mostly concerned in the device simulation and then discuss the composition dependence in terms 

of mole fraction. Beside, the lattice temperature effect on some parameters will also be mentioned. 

The minimum set of material parameters which have to be known in order to proceed the 

device simulation include: 

1. Electron affinity, χ , and conduction band edge offset due to the composition change. 

2. Energy bandgap, E g . 

* * 

3. Effective masses for electrons and holes, m n and m p , from which the effective densities of states 

for the conduction and valence bands, N C and N V , can be derived (Eq. (2.4)). 

4. Static and high-frequency dielectric constants, and . 

ε 0 

ε ∞ 


Material Properties for Heterostructures 

5. Electron and hole mobilities, µ n and µ p , and their dependence on composition, doping density, 

electric field, and temperature. 

6. Minority carrier lifetime and corresponding coefficients for various recombination mechanisms 

including Auger and radiative. 

7. Coefficients for the impact ionization. 

8. Saturation velocity, , which is used as a parameter in certain field-dependent mobility models. 

v sat 

Before we address the detailed values and dependence of these parameters, however, we will 

first discuss the interpolation scheme for determining the compound material parameters based on the 

knowledge of the base materials which constitute the compound. 

4.2 Interpolation Scheme for Composition 

Dependence 

The parameters for ternary materials can be determined using the linear interpolation scheme from 

those of the constituent binary materials. But often this simple scheme is not accurate enough and the 

quadratic term, which is available for some materials from experimental data, has to be included. For 

examples, refer to Eq. (4.5) and other formulation for energy bandgaps in Section 4.4.1. The material 

parameters for quaternaries can be determined from those of ternaries using the following interpolation 

scheme. 

Qxy ( , ) 

1 

= --------------------------------------------- ⋅ 

x( 1 – x) + y( 1 – y) 

{ 

x( 1 – x) [( 1 – y)T Gax In 1 – x P + yT Gax In 1 – x As] + 

y( 1 – y) ( 1 – x) [( 1 – x)T InAsy P 1 – y 

+ xT GaAsy P 1 – y 

]} 

where Ga x In 1-x As y P 1-y is used as an example for quaternary material. We now provide a number of 

material parameters in PISCES-2ET as discussed below. 

(4.1) 



4.3 Data for Material Parameters 

4.3.1 Parameters for Base Materials 

Currently PISCES-2ET can handle four material systems: Ge x Si 1-x , Al x Ga 1-x As, Al x In 1-x As, and 

Ga x In 1-x As y P 1-y . Those compound materials can be derived from four types of base materials: Si, 

GaAs, InAs, and InP. A partial list of their respective material parameters are given in th following. 

Table 4.1 

E g 

† 

E g 

α 

β 

ε 0 

ε ∞ 

χ 

m n 

* 

* 

m lh 

* 

m hh 

N C 

† 

N V 

† 

µ n 

† 

µ p 

† 

† 

v sat 

Si GaAs InAs InP units 

1.08 [23] 1.424 [24] 0.359 [28] 1.347 [26] eV 

1.17 [24] 1.519 [24] 0.4105 [28] 1.4205 eV 

4.73 [24] 5.405 [24] 3.35 [29] 4.1 10 -4 eV/K 

636 [24] 204 [24] 248 [29] 136 K 

11.8 [25] 13.1 [24] 14.55 [29] 12.4 [26] 

10.9 12.25 [28] 9.55 [26] 

4.17 [23] 4.07 [24] 4.9 [29] 4.4 [29] eV 

1.08 [25] 0.067 [26] 0.023 [26] 0.08 [26] 

0.16 [24] 0.074 [26] 0.024 [29] 0.089 [26] 

0.49 [24] 0.62 [26] 0.41 [29] 0.85 [26] 

19 

17 

m 0 

m 0 

m 0 

2.8×10 [24] 4.42×10 8.72×10 5.66×10 cm – 3 

19 

18 

1.04×10 [24] 8.47×10 6.66×10 2.03×10 cm – 3 

1500 [24] 8500 [24] 22600 [29] 4500 [29] cm 2 /V.s 

450 [24] 400 [24] 250 [27] 150 [29] cm 2 /V.s 

7 

7 

16 

18 

1.5×10 [27] 1×10 [23] 2.5×10 

[23] cm/ s 

7 

17 

19 

† T L = 300 K 

The lattice temperature dependent energy bandgap is modeled as follows: 



2 

αT 

E g ( T L ) = E g0 – --------------- L 

(4.2) 

β + T L 

where T L is in K. When the data for the light and heavy holes are available, the overall hole effective 

mass used in the program is determined by 

*3 ⁄ 2 

m p 

*3 ⁄ 2 

*3 ⁄ 2 

m hh 

= m lh + 

(4.3) 

We have also defined three auxiliary materials: Ge, AlAs, and GaP, which are used to constitute the 

desired ternaries and quaternary. Their material parameters relevant to simulation are listed below: 

Table 4.2 

Parameters Ge AlAs GaP units 

E g 

† 

E g0 

α 

β 

ε 0 

ε ∞ 

χ 

m n 

* 

* 

m lh 

* 

m hh 

N C 

† 

N V 

† 

† T L = 300 K 

0.67 [25] 2.14 [28] 2.24 [25] eV 

0.744 [24] 2.23 [28] 2.4 [25] eV 

4.77 [24] 4.0 [28] 5.4 [25] 10 -4 eV/K 

235 [24] K 

15.8 [25] 10.06 [28] 10.2 [25] 

8.16 [28] 8.90 [29] 

4.0 [25] 3.62 [23] 4.0 [29] eV 

0.55 [25] 0.124 [28] 0.17 [26] 

0.044 [24] 0.26 [28] 0.14 [26] 

0.28 [24] 0.5 [28] 0.79 [26] 

19 

m 0 

m 0 

m 0 

1.04×10 [24] 

cm – 3 

18 

6.0×10 [24] 

cm – 3 

Now we discuss how the parameters for the compound materials are determined, starting with 

the bandgap. 



4.4 Band Structure Parameters 

4.4.1 Bandgap 

We will discuss first those compound semiconductors which need only one mole fraction to determine 

the composition, that is, either Ge x Si 1-x or ternaries. For Ge x Si 1-x , currently only the data for the 

strained layer [30] is accessible in the program. The formulation is as follows (in units of eV): 

E g ( x) = 

1.16 – 0.945 

E gSi , – -----------------------------x 

0.245 

x ≤ 0.245 

= 

0.945 – 0.87 

0.945 – ----------------------------- ( x – 0.245) 

0.35 – 0.245 

0.245 < x ≤ 0.35 

= 

0.87 – 0.78 

0.87 – -------------------------- ( 

0.5 – 0.35 

– 0.35 ) 0.35 < x ≤ 0.5 

0.78 – 0.72 

= 0.78 – -------------------------- ( 

0.6 – 0.5 

– 0.5 ) 

0.5 < x ≤ 0.6 

= 

0.72 – 0.69 

0.72 – -------------------------- ( x – 0.6) 

0.675 – 0.6 

0.6 < x ≤ 0.675 

= 

0.69 – 0.66 

0.69 – -------------------------------- ( x – 0.675) 

0.735 – 0.675 

0.675 < x ≤ 0.735 

= 0.66 

x > 0.735 

(4.4) 

For Al x Ga 1-x As, simply use 

E g ( x) = 1.424 + 1.247x 

x ≤ 0.45 (direct band) 

= 1.900 + 0.125x + 0.143x 2 x > 0.45 (indirect band) 

(4.5) 

For bandgap of Al x In 1-x As, as x is increased from 0 to 1 the band structure also undergoes a 

transition from the direct to indirect bandgap and the critical composition is x = 0.56 . The expression 

for E g at room temperature is as follows [31]: 

E g = 2.95x + 0.36( 1 – x) – 0.7x( 1 – x) 

x ≤ 0.56 (direct) 

= 2.16x + 1.37( 1 – x) – 0.7x( 1 – x) 

x > 0.56 (indirect) 

(4.6) 



where when x < 0.56 the (direct) bandgap is determined by the Γ valley of the conduction band 

( E g ( AlAs) = 2.95eV , E g ( InAs) = 0.36eV ), and when x > 0.56 the (indirect) bandgap is 

determined by the X valley ( E g ( AlAs) = 2.16eV , E g ( InAs) = 1.37eV .) 

Before giving the expression for the bandgap in the quaternary Ga x In 1-x As y P 1-y . we first list 

the expressions for the bandgaps of four ternary materials, on which Ga x In 1-x As y P 1-y is based. 

E g ( Ga x In 1 – x P) = 1.35 + 0.643x + 0.786x 2 

E g ( Ga x In 1 – x As) = 0.36 + 0.505x + 0.555x 2 

E g ( InAs y P 1 – y ) = 1.35– 1.083y + 0.091y 2 

E g ( GaAs y P 1 – y ) = 2.74– 1.473y + 0.146y 2 

(4.7) 

(4.8) 

(4.9) 

(4.10) 

And for the strained Ga x In 1-x As layer, the bandgap is evaluated according to the expression 

provided by Corzine et al. [32]: 

E g ( Ga x In 1 – x As) = 1.424 – ( 1 – x) { 1.061 – ( 1 – x) [ 0.07 + 0.03( 1 – x) 

]} 

(4.11) 

If either x or y in Ga x In 1-x As y P 1-y has the value of zero or one, then one of the expressions, 

Eqs. (4.7) - (4.10), is used to evaluate the bandgap, otherwise the following general formula is used to 

evaluate the (lowest-direct) bandgap in Ga x In 1-x As y P 1-y [26]: 

E g ( x, 

y) 

1 

= --------------------------------------------- { 

x( 1 – x) + y( 1 – y) 

x ( 1 – x )[( 1 – y)E g ( Ga x In 1 – x 

P) + yE g ( Ga x In 1 – x 

As) 

] 

+ y( 1 – y) ( 1 – x) [( 1 – x)E g ( InAs y P 1 – y ) + xE g ( GaAs y P 1 – y )]} 

The values obtained from the above expression is for room temperature ( = 300K ). 

T L 

(4.12) 

4.4.2 Electron Affinity and Band-edge Offsets 

The band edge offsets caused by the composition change are critical in determining the heterostructure 

device characteristics. In PISCES-2ET, the band edge offsets are actually accounted for by the change 

of the electron affinity and the bandgap. Even in the homogeneous material, if the bandgap narrowing 

occurs due to the heavy doping effect, the band edges shift towards the center of the bandgap. It is 



usually assumed in this case that the amount of the edge shift for both the conduction and valence 

bands are the same. For the current implementation, except of Al x Ga 1-x As, Al x In 1-x As, and Ga x In 1- 

x As y P 1-y , it is assumed that all bandgap change due to the composition change occurs only at the 

valence edge due to the lack of sufficient experimental data. However, the bandgap narrowing due to 

the heavy doping effect, is accounted for in the aforementioned manner for all materials, i.e., evenly 

split. For Al x Ga 1-x As / GaAs, ∆E C : ∆E V is taken as 0.6 : 0.4 and for Al x In 1-x As / InAs, 0.706 : 0.294, 

where ∆E is considered positive when the band edge is expanding, that is the bandgap becomes larger. 

For Ga x In 1-x As y P 1-y / InP the bandgap change is simply assumed evenly split among the conduction 

and valence bands edges 1 . By designating the percentage of the shift of conduction band edge with 

respect to the bandgap change as γ, we have the following relationship for the electron affinity as 

function of the mole fractions: 

χ( x, 

y) = χ( 00 , )– 

γ[ E g ( x, 

y) – E g ( 00 , )] 

(4.13) 

For ternaries, y does not appear in the formula. And 

∆E C 

= 

– ∆χ 

(4.14) 

∆E V = ∆χ + ∆E g 

(4.15) 

4.4.3 Effective Mass and Density of States 

The calculation of the effective density of states is based on the density-of-state effective mass, which 

in turn depends on the mole fraction. Moreover, one needs to consider for electrons the effective 

masses at different valleys in the conduction band and for holes the light and heavy masses in order to 

construct the overall effective masses used in computing the densities of states. We use a different 

formulation to compute effective masses for each different material system based on our best 

knowledge. For Al x Ga 1-x As / GaAs material system, since we know composition dependence of 

electron effective mass and band gap at each valley (Γ, L, and X), we can use weighted scheme to 

compute the electron effective mass (for details, see [33]). And for holes, the following linear formula 

is used: 

1. ∆E C = ( 71± 

7)%∆E g is measured for Al 0.48 In 0.52 As / Ga 0.47 In 0.53 As in [34]. 



( x) 

-------------- = 0.48 + 0.31x 

m p * 

m 0 

(4.16) 

For Al x In 1-x As / InAs system, we simply use the linear interpolation scheme for both 

electrons and light and heavy holes. That is, 

* 

* 

xm AlAs 

m * ( x) = ( 1 – x)m InAs + 

(4.17) 

where the effective masses for InAs and AlAs can be found in Table 4.1 and Table 4.2, respectively. 

For Ga x In 1-x As y P 1-y / InP, the interpolation scheme based on the constituent binaries is used 

for obtaining the effective masses for electrons and light and heavy holes. For electrons, we don’t 

distinguish between the bulk and the strained layer. The interpolation scheme is as follows: 

m n 

* 

= 

* 

( 1 – x)ym n, 

InAs 

* 

xym n, 

GaAs 

+ ( 1 – x) ( 1 – y)m n, 

InP + 

+ x( 1 – y)m n, 

GaP 

* 

* 

(4.18) 

For holes, the effective masses of the light and heavy holes in the bulk material are calculated 

in the same manner. However, for the strained layer, they are taken as constants according to Corzine 

in [35] 1 . 

* 

m lh 

= 

0.078m 0 

(4.19) 

* 

m hh 

4.5 Dielectric Constants 

= 0.165m 0 

(4.20) 

Different interpolation schemes are used for different compound materials. For ternaries Al x Ga 1-x As 

and Al x In 1-x As, we use the same scheme as in SEDAN [33] for Al x Ga 1-x As. That is, by knowing the 

dielectric constants at high and low frequencies for the constituent binaries, the respective dielectric 

constant is evaluated using 

1. We have intentionally flipped the data for the light and hole holes because of suspicion of the mistake 

incurred in the cited paper. 



1 2 x ε 1 – 1 

------------- ( 1 – x) ε 2 – 1 

+ + ------------- 

ε 

ε 

1 + 2 ε 2 + 2 

= ------------------------------------------------------------------------ 

1 x ε 1 – 1 

– ------------- ( 1 – x) ε 2 – 1 

– ------------- 

ε 1 + 2 ε 2 + 2 

(4.21) 

where ε 1 

is that of AlAs for both the materials, and ε 2 

is that of GaAs for AlGaAs and of InAs for 

AlInAs. The formulation applies to both high and low frequencies. 

The dielectric constants for Ge x Si 1-x are obtained by using the linear interpolation for those 

of Ge and Si. For the quaternary Ga x In 1-x As y P 1-y , the interpolation scheme in Eq. (4.18) is used based 

on the data for the constituent binaries. 

4.6 Mobilities 

Due to the lack of experimental data, the mobility dependences on composition, doping, lattice 

temperature, and field are not complete for most of the compound materials. Whenever data are not 

available constant mobility as listed in Section 3.1.1.1 is used. Readers are referred to [29] for data for 

many other materials, even though the collection of data is rather out-of-date (1971). 

4.7 Impact Ionization 

For relevant formulas and material parameters, see Section 3.3.1.1. 




CHAPTER 5 

Numerical Techniques 

In this chapter various numerical techniques and data structure will be discussed. Since the 

development of PISCES has spanned over a decade, we only address here the improvement over the 

previous versions (II and II-B). Interested readers are referred to reports [3] and [4]. 

5.1 High and Zero Frequency AC Analyses 

The algorithm for AC analysis in the device simulation mostly follows Laux’s approach [36] and is 

based on the perturbation method applied to the DC solution. Before we discuss the improvement in 

the original implementation (PISCES IIB), the mathematical essence of the AC analysis is first 

described. 

5.1.1 General Principle of AC Small Signal Analysis 

Consider x as the column vector of all the basic variables to be solved such as ψ, n and p, and column 

vector p represents all the applied terminal bias, the task of DC analysis can be considered as the 

solution to the following nonlinear, algebraic equation: 

F( x, 

p) = 0 

(5.1) 

where both the equation vector (also a column vector) F and variable vector x have dimension of N, 

the number of all basic variables in the simulation region, i.e., F, x ∈ R N , while the parameter vector 



p has the dimension of M, no bigger than the total number of the device terminals, or p ∈ 

analyses involving the time evolution such as transient and AC analyses, the above equation must be 

modified to include the time derivative part. Thus, 

R M 

. For 

where 

F + f = 0 

(5.2) 

f = D ∂ ----- 

x 

(5.3) 

∂t 

where D is a diagonal matrix (N× N) with rows corresponding to the Poisson’s equation zero and others 

–1 . We now apply bias of form 

p = p+ 

p˜ e jωt 

(5.4) 

That is, an AC signal of angular frequency ω and amplitude p˜ (notice that the multi-dimensionality 

represents the bias at all terminals) which is generally a vector of complex numbers, superimposed on 

the DC bias, p. The response, that is the solution vector x, should also have the form of 

x = x + x˜ e jωt 

(5.5) 

where vector x is the DC response and are the real numbers, and x˜ is a phasor vector and are complex 

numbers due to the change of phase in response to the input signal. For the small signal analysis, 

p˜ → 0 where represents the norm of the vector, hence x˜ → 0 . Substituting Eqs. (5.4) and (5.5) 

into Eq. (5.2) and applying the Taylor expansion to Eq. (5.2), by retaining only terms which have the 

first order of e jωt on obtains the following equation: 

F( x, 

p) + [ F x ( x, 

p)x˜ + F p ( x, 

p)∆p + jωDx˜ ]e jωt = 0 

(5.6) 

Note that in the above we have replaced p˜ with a real number vector ∆p , i.e. we assume all the input 

signals are in the same phase. Furthermore, because both x and p are vectors the derivatives of F x 

and F p are actually matrices with F x being a square one while F p is generally not. 

With the DC solution already known, i.e. 

following: 

F( x, 

p) = 0 , Eq. (5.6) can be simplified to the 

( + jωD)x˜ = – F p ∆p 

F x 

(5.7) 



and the only unknown variable is x˜ , the AC response. Because x˜ is a complex number, we can write 

x˜ = x r + jx i where x r and x i are real and imaginary parts, respectively, and j = – 1, Eq. (5.7) then 

becomes a set of two equations in real number mathematics: 

F x x r – ωDx i = – F p ∆p 

(5.8) 

ωDx r + F x x i = 0 

(5.9) 

These two equations are coupled to each other so to find x r 

and x i 

, they have to be solved 

simultaneously in principle. Because each of vectors x r 

and x i 

has dimension of N, then we must solve 

a system of equations with dimension of 2N × 2N which needs to quadruple the memory storage as is 

required for the DC analysis. Because the AC analysis is usually not performed as routinely as the DC 

analysis, to set aside a large trunk of memory space solely for the AC analysis is not an economic 

choice especially when the program is not written to take the advantage of dynamic memory allocation. 

It is preferable, therefore, to use an iterative method to solve the above equation. One popular method, 

also the one used in PISCES IIB is the so-called SOR (Successive Over-Relaxation) method [36]. The 

essence of this method can better be seen from the following matrix equation form: 

⎛J 

– ωD⎞⎛x r ⎞ ⎛B⎞ 

Ax = ⎜ 

⎟⎜ 

⎟ = ⎜ ⎟ 

(5.10) 

⎝ ωD J ⎠⎝x i ⎠ ⎝ 0⎠ 

where we have altered the symbols used in Eqs. (5.8)-(5.9) with the Jacobian matrix J = F x and the 

stimulus B = – F p ∆p which has non-zero (real number) terms only for rows corresponding to the 

Poisson’s equation. If the magnitude of the off-diagonal elements, i.e., ω D, in the above block matrix 

equation are small compared to the diagonal elements, then the iterative approach by repeating the loop 

of first solving 

J x r = B + ωDx i 

for x r 

while fixing x i 

and then solving 

(5.11) 

J x i = – ωDx r 

(5.12) 

for x i 

using the recently updated x r 

, will converge easily. But as the ω increases, the convergence 

becomes poorer and eventually fails to converge when the frequency approaches the cutoff frequency, 

f T 

, of the device under analysis [36]. A final note regarding SOR method is the use of relaxation factor. 



Instead of employing the above simple iteration procedure (Eqs. (5.11) and (5.12)), the actual iteration 

takes form of 

k + 1 

x r 

= 

k 

( 1 – ν)x r 

νJ – 1 

k 

+ ( B + ωDx i ) 

(5.13) 

k + 1 

k 

x i ( 1 – ν)x i νJ – 1 k + 1 

= + (– ωDx r ) 

(5.14) 

where ν is the relaxation factor and its value ranges from 0 to 2, and k is the iteration count. When 

ν = 1 , Eqs. (5.13) and (5.14) are reduced to Eqs. (5.11) and (5.12). One of the most challenging tasks 

in SOR method is to determine the optimized value of ν and we will discuss later other iteration 

schemes which avoid using the relaxation factor at all. 

5.1.2 Matrix Transformation to Improve Diagonal Dominance 

The diagonal dominance of the coefficient matrix for the linear equation system at high frequency can 

be improved by performing a matrix transformation or called pre-conditioning. A properly chosen 

matrix T is left-multiplied to the both sides of (5.10) such that the resulted coefficient matrix, 

A T = TA, will have a better or roughly the same diagonal dominance when the frequency increases. 

This transformation matrix can indeed be constructed as follows. Considering the coefficient matrix A 

in Eq. (5.10) as a 2× 

2 block matrix, the presence of the off-diagonal blocks with opposite signs 

actually enhances the determinant of the entire matrix. This observation suggests the use of the 

following transformation matrix [37]: 

I 

– 1 

⎛ 

ωDD 

T 

J 

⎞ 

= ⎜ – 1 

⎟ 

(5.15) 

⎝– 

ωDD J I ⎠ 

where I is the identity matrix and D J 

is the diagonal matrix consisting of only the diagonal elements in 

J. The resulting equation is thus 

J ω 2 DD – 1 

1 

⎛ + J D ωDD – J J 0 ⎞⎛x r ⎞ ⎛B⎞ 

A T x = ⎜ 

⎟⎜ 

⎟ = ⎜ ⎟ 

1 

– ωDD J J ω 2 1 

⎝ 

+ DD – J D⎠⎝x i ⎠ ⎝ 0⎠ 

– J 0 

(5.16) 



where J and the property of has been used to arrive at the above equation 1 0 = J – D J 

DB = 0 

. Note 

– 1 

that because D J is a diagonal matrix so its inverse D J is trivial to compute. It becomes immediately 

clear from Eq. (5.16) that although the magnitude of the off-diagonal blocks still increases 

proportionally with ω, that of the diagonal entries may increase even faster due to the additional term 

which is proportional to 

ω 2 

, thus avoiding the problem of diagonal blocks being overwhelmed by the 

off-diagonals. There are three distinctive ranges of frequencies where the transformed matrix shows 

different characteristics. At low frequencies, which can be quantified by all the non-zero entries in 

– 1 

ωDD J being much less than unity, off-diagonal blocks can be considered as small perturbations with 

respect to the diagonal blocks and iterative algorithms should do well with or without the 

– 1 

transformation. At very high frequencies, where all the non-zero entries of ωDD J are much greater 

than unity, the enhancement to the diagonal blocks makes the entire matrix become increasingly 

diagonally dominant, which implies the improved performance for the iterative algorithm. At the 

intermediate frequencies between these extremes, however, the situation is not as clearly cut since the 

off-diagonal blocks can no longer be considered as small perturbations while the growth in the 

enhancements to the diagonal blocks has not caught up with the growth in the off-diagonals. 

5.1.3 Pre-conditioned TFQMR Method for AC Analysis 

As mentioned in Section 5.1.1, the choose of an optimized relaxation factor in SOR method is a 

difficult task. It is, therefore, much preferable to have an iterative method which does not require any 

relaxation factor, yet still keep the efficient usage of the memory space. In PISCES-2ET, we employ 

an iterative method called TFQMR (Transpose-Free Quasi-Minimal Residual) method [38]. The major 

difference from the conventional SOR method is, in addition to the elimination of the relaxation factor, 

that it updates the entire solution array, ( , ) T , simultaneously. Before we describe the detailed 

x r 

x i 

procedure flow of this method, however, we will discuss the pre-conditioning technique further more. 

For any iterative method to converge fast in solving linear equation system, it is always desirable to 

have a near identity coefficient matrix. The near identity of a matrix can be achieved by preconditioning, 

that is, to multiply a certain matrix (called pre-conditioner) on the both sides of the 

equation. A simple and natural choice of the pre-conditioner would be the block diagonal matrix 

derived from the original coefficient matrix. With such a pre-conditioner, only back substitutions are 

1. The right hand side of Eq. (5.10) has been multiplied by T but the result remains the same as the 

original. 



needed during iteration. Designating the pre-conditioner as P = M – 1 , then the matrix M for Eq. (5.16) 

will be 


M 

= 

– D 

J ω 2 1 

⎛ + DD 

⎜ 

J 

⎝ 0 

0 

– D 

J ω 2 1 

+ DD J 

⎞ 

⎟ 

⎠ 

(5.17) 

⎛J 0 ⎞ 

M = ⎜ ⎟ 

(5.18) 

⎝0 J ⎠ 

for Eq. (5.10). Readers can verify that by using these pre-conditioners, the resulting coefficient 

matrices have identity matrices as their diagonal blocks. At the low frequency, the off-diagonal blocks 

are very small in magnitude, leading to a quick convergence. 

As an iterative algorithm, the SOR method has the advantage of simplicity and minimal 

requirement for the data storage. In practice, however, we have found that a proper relaxation 

coefficient is difficult to obtain. In contrast, there are several attractive advantages with the so-called 

QMR (Quasi-Minimal-Residual) iterative algorithm [39]. Until quite recently, all existing iterative 

algorithms either use non-minimization procedure in generating the update vectors, which results in a 

very volatile residual reduction process, or use a full minimization procedure which requires 

increasing data storage as the iteration proceeds. By applying a quasi-minimal residual approach, 

QMR is able to retain the advantage of requiring only the fixed amount of data storage. At the same 

time, the residual reduction process becomes very smooth with only occasional, insignificant 

increases. Furthermore, like all other Krylov subspace methods based on the Lanzos vectors, no 

external parameters are needed [39]. The particular QMR algorithm we have implemented in PISCES- 

2ET is the TFQMR (Transpose-Free Quasi-Minimal-Residual) [38] with the pre-conditioner M in 

either Eq. (5.17) or Eq. (5.18) applied before iteration. The detailed procedure of TFQMR with preconditioner 

M is summarized as follows: 

1. Initialization: 

(a) b = M -1 B; 

(b) y 1 = u 0 = r 0 = r˜ = b, x 0 = d 0 = 0; 



(c) ρ 0 = τ 0 = r 0 , θ 0 = η 0 = 0 ; 

2. For n = 12… , , do 

ν n – 1 M – 1 Ay 2n – 1 

(a) = 

; 

(b) σ n – 1 = r˜ ⋅ v n – 1 , α n – 1 = ρ n – 1 ⁄ σ n – 1 ; 

(c) y 2n = u n – 1 – α n – 1 v n – 1 ; 

(d) r n = r n – 1 – α n 1 ( – + y 2n – 1 ) ; 

(e) ω 2n + 1 = r n , ω 2n = r n ⋅ r n – 1 ; 

(f) For m = 2n – 1, 

2n do 

• d m = y m + ( θ m – 1 η m – 1 ⁄ α n – 1 )d m – 1 ; 

2 

• θ m = ω m + 1 ⁄ τ m – 1 , c m = 1 ⁄ 1+ 

θ m ; 

• τ m = ω m + 1 

c m , η m = c 2 m α n – 1 ; 

• x m = x m – 1 + η m d m ; 

•Ifx has converged: stop. 

(g) ρ n = r˜ ⋅ r n , β n = ρ n ⁄ ρ n – 1 ; 

(h) u n = r n + β n y 2n ; 

(i) y 2n + 1 = u n + β n ( y 2n + β n y 2n – 1 ) ; 

In [38], 1 + mτ m is given as an upper limit for the residual norm. In our implementation, the 

residual norm is initially assumed to be equal to τ m (a coefficient of unity). When τ m drops below the 

tolerance, the true residual norm is evaluated, which also gives out the real proportional coefficient 

between the residual norm and 

– M – 1 Au n 1 

2 

τ m 

. If the residual norm is not below the tolerance, the iteration 

continues with the new coefficient. 

The effectiveness of the TFQMR with pre-conditioning in AC analysis has been tested in an 

analysis of GaAs MESFET [40]. There is essentially no limitation as to how high the frequency can 



be applied to the device during simulation and the agreement between the measured and simulated 

results are very good. 

5.1.4 Zero Frequency AC Analysis 

As the conclusion of this section, we present a special case in the AC analysis where a direct method 

can be used and the results of this type of analysis have broad applications. This is the case when the 

frequency approaches zero. In this case, x r 

can be found directly from Eq. (5.8) by setting ω = 0 . It 

would be tempted to conclude that x i = 0 from Eq. (5.9) using the same reasoning. By doing so, 

however, valuable information will be lost. Consider the case where x i 

is proportional to the frequency, 

which actually often occurs in the device characterization. For example, in capacitance x i = ωC . The 

linear coefficient can then be extracted from solving Eq. (5.9) even when ω → 0 . A practical 

application would be the evaluation of the junction capacitance including both the depletion and 

diffusion components. Thus by assuming x i = ωC where C is an array of trans-capacitances, one can 

find C by solving the following equation 

F x C = – Dx r 

(5.19) 

Information such as the change of the storage charge from the quasi steady state analysis can 

thus be obtained by using the zero-frequency AC analysis, which involves only two more solutions of 

a linear equation with the coefficient matrix the same as the Jacobian for the DC solution but different 

right hand side terms. 

5.2 Discretization Scheme for Carrier and Energy 

Fluxes 

In assembling the node equations for continuity equations, a key issue is to express the carrier/energy 

flux along the grid line using the variables on the two ends of the line. A classic discretization scheme 

for the current (or the carrier flux) as function of the carrier density and potential is the Scharfetter- 

Gummel discretization scheme. Now the carrier and lattice temperatures are also introduced as the 

basic variables, we need to re-examine the original scheme. The discretization form for the carrier flux 

from node 1 to node 2 along the grid line linking these two nodes is as follows when the temperature 

effects are taken into consideration: 



1 

F n, 1→ 

2 = 

d 21 

1 

F p, 1 → 2 = 

d 21 

------ [ µ n2 Bu ( n, 

21 )n 2 T n2 – µ n1 B( – u n, 

21 )n 1 T n1 ] 

------ [ µ p1 Bu ( p, 

21 )p 1 T p1 – µ p2 B( – u p, 

21 )p 2 T p2 ] 

where F n = – j n ⁄ q and F p = j p ⁄ q, and B is the Bernoulli function defined as 

u c 21 

x 

Bx ( ) = ------------- 

e x – 1 

is the function of the potential difference and carrier temperature defined as follows: 

(5.20) 

(5.21) 

(5.22) 

, 

u c 21 

ψ 2 – ψ 

, = ---------------------------------- 1 

(5.23) 

( T c1 + T c2 ) ⁄ 2 

where c stands for either n or p and d 21 

is the distance between nodes 1 and 2. The assumptions made 

in the above discretization scheme are: 

1. Mobility is constant along the grid line between nodes 1 and 2 (called as interval) and its value 

is the average of the mobilities on two nodes. 

2. E( x) ⁄ T c ( x) 

≈ const over the interval where x represents the position within the interval. In 

particular, 

E ψ 1 – ψ 2 2 

----- = ------------------ ---------------------- 

T c 

d 21 T c1 + T c2 

3. Flux, F, is constant over the interval. 

(5.24) 

The discretization for energy flux is as follows: 

1 

s n, 1→ 

2 

d 21 

ψ 

------ µ n2 Bu ( n, 

21 )n 2 T 1 + ψ = ⎛ 2 

n2 ------------------ – c 

2 e T ⎞ 

⎝ 

n2 – 

⎠ 

µ n1 B( – u n, 

21 )n 1 T ⎛ψ 1 + ψ 2 

n1 ------------------ – c 

2 e T ⎞ 

⎝ 

n1 ⎠ 

(5.25) 



1 

s p, 1 → 2 

d 21 

ψ 

------ µ p1 Bu ( p, 

21 )p 1 T 1 + ψ = ⎛ 2 

p1 ------------------ – c 

2 e T ⎞ 

⎝ 

p1 – 

⎠ 

µ p2 B( – u p, 

21 )p 2 T ⎛ψ 1 + ψ 2 

p2 ------------------ – c 

2 e T ⎞ 

⎝ 

p2 ⎠ 

(5.26) 

flux: 

where c e = 5 ⁄ 2– 

ν 

1 and is set to a default value of 1.8 in the code. The form for the heat 

κ 

F heat, 1→ 

2 = 

d 21 

------ ( T L1 – T L2 ) 

where the average κ over the interval is evaluated as follows: 

(5.27) 

5.3 Normalization 

T L1 + T L2 

κ L = κ ⎛ 

0 

----------------------- 

⎝ 2 × 300 ⎠ 

⎞ – α 

(5.28) 

This section briefly describes the normalization scheme used in PISCES-2ET. Internal variables 

representing basic variables: ψ (as well as φ’s for quasi Fermi potentials), n, p, T n 

, T p 

, and T L 

, are all 

normalized before they are used in the computation. Potentials are normalized by V th = k B T 0 ⁄ q 

where T 0 

is the environment temperature which can be accessed through parameter temperature 

in the model card. All temperatures are normalized using the environment temperature and carrier 

concentrations are normalized using c scl = N C N V where N C 

and N V 

are for the base semiconductor 

material 2 . The current density is normalized using the quantity of –qc scl V th . The reason for choosing 

this normalization factor is related to the use of Scharfetter-Gummel scheme and minus sign is incurred 

because the electron current density is used as the reference. Other quantities such as distance, time, 

electric field, mobility are not normalized. 

1. For meaning of ν see Eq. (A.27) in APPENDIX A. 

2. There is only one base material for a simulated region even though there might be several material 

systems in the device. 



5.4 Newton Projection Scheme 

Newton projection scheme is a method to project the next solution based on the current solution when 

the applied bias is changed. It has also application in low-frequency, small signal analysis. The 

principle of this scheme is rather simple and is described in this section. Again taking Eq. (5.1), but 

now we only consider the DC case. When bias is advanced, i.e. 

p = p + ∆p 

one can obtain the following approximate equation: 

F( x + ∆x, 

p + ∆p) ≈ F( x, 

p) + F x ( x, 

p)∆x + F p ( x, 

p)∆p 

= 0 

(5.29) 

(5.30) 

Because the solution at p has been found, i.e., F( x, 

p) = 0 , the increment of x due to p can 

be found by solving the following system of equations: 

F x ∆x 

= 

– F p ∆p 

(5.31) 

This is a linear system of equations with the same coefficient matrix as for the DC solution 

and F p is easy to find because F has few equations which are related to p. The above formulation can 

also be applied to the low-frequency small signal analysis because when ∆ p → 0, the ratio of ∆x ⁄ ∆p 

can be found exactly by solving the above equation for ∆x. Foe more detailed discussion of this 

method, readers are referred to [41]. 

5.5 Global Data Structure in PISCES-2ET 

This section describes how one can change the maximum number of grid points in the simulator. Since 

PISCES-2ET is coded using Fortran 77, memory usage is static and knowledge of various array sizes 

is necessary during the compilation time. All of the basic dimensions are defined in the common file 

p2conf.h and are written in a fully scalable way. The first part of p2conf.h reads as follows: 

-------------------------p2conf.h------------------------------ 

c There are four parameters that affect the memory usage of 

c PISCES-2ET: 

c AVGNB - average neighbors of each node point including 

c 

itself. For a quad-based mesh with control level 



c 

equal to 1, 6 neighbors are a very conservative 

c 

estimation (can be higher for pure Delaunay mesh.) 

c MAXPDE - max. no. of equations solved (1 for Poisson only, 

c 

6 for DUET) 

c MAXPT - max. no. of grid points in the simulated device 

c MAX1D - bandwidth of the LU-factored Jacobian. Since 

c 

minimum degree (fill-in) is employed, the worst 

c 

case will be sqrt(MAXPT). If the device is highly 

c 

1-D oriented, MAX1D can be much smaller to improve 

c 

memory efficiency. 

c 

integer AVGNB, MAXPDE, MAXPT, MAX1D 

parameter (AVGNB = 6, MAXPDE = 3) 

parameter (MAXPT = 3000, MAX1D = 55) 

c parameter (MAXPT = 6000, MAX1D = 78) 

c parameter (MAXPT = 9000, MAX1D = 95) 

--------------------------------------------------------------- 

The total memory usage during the run time of PISCES-2ET is approximately: 

16 * MAX1D * MAXPDE * MAXPDE * MAXPT (in bytes) 

Note that since the full Newton iteration is the default method owing to its robustness, the 

memory space required is proportional to the square of the number of equations and to the power 1.5 

of the number of points in the worst case (when MAX1D is equal to the square root of the number of 

points, i.e., the mesh points are evenly distributed in X and Y directions). The present setup (MAXPT 

= 3000) will take about 24M-byte memory space. Since most of the memory allocation is shared in 

a common block called “tmpco” (in various.h files), users can still run DUET model with the present 

setup at least to about 1,200 points. Most of the modern workstations have more than 24M-byte main 

memory, so the swapping during execution should be minimal. If the application cannot be bounded 

by this setup, users need only to change the above four parameters and remake (recompile) the 

PISCES-2ET executable. PISCES-2ET will automatically report any insufficient memory allocation 

during the first encounter (usually at the symbolic factorization). Users can then modify the reported 

dimensions and make further trade-off accordingly. If the application is always much smaller than the 

present setup, we do not suggest to recompile. If MAXPT becomes too small and the factored LU 

matrix in full Newton iteration is no longer dominant in the memory usage, users probably will have 

some complaints from the compiler about array with negative dimensions. This is because the common 



“tmpco” space is shared in many routines and the patch array TMPPAD is used to make every 

common declaration to have the same length to avoid compiler errors. If users have to do this (probably 

due to an old 8MB main memory machine) and the compiler indeed complains the negative dimension, 

users need to change the last line in p2conf.h, where the size of the common block “tmpco” is 

defined symbolically. Other constraints will have minimal impact on the memory usage. They are 

listed below for reference. 

---------------------p2conf.h-------------------------- 

c 

c OTHER GLOBAL CONSTRAINTS ON DIMENSION 

c 

integer MAXCON, MAXCNT, MAXNB, MAXPAR 

integer MAXINF, MAXREG, MAXREC, MAXPTORI, MXBDEP 

c.. maximum number of contact nodes 

parameter (MAXCON = 500) 

c.. maximum number of contacts 

parameter (MAXCNT = 10) 

c.. maximum number of triangles a point can belong to 

parameter (MAXNB = 20) 

c.. maximum number material parameters 

parameter (MAXPAR = 50) 

c.. maximum number of interfaces 

parameter (MAXINF = 10) 

c.. maximum number of regions 

parameter (MAXREG = 1000) 

c.. maximum elements in 1-D for temporary tensor-product 

c grid info 

parameter (MAXREC = 1000) 

c.. maximum depth of bias partition 

parameter (MXBDEP = 10) 

c.. maximum original tensor-product mesh points before 

c elimination 

parameter (MAXPTORI = 10*MAXPT) 

--------------------------------------------------------- 

The remaining dimension declaration is defined symbolically. 




CHAPTER 6 

Simulation Examples 

In this chapter, four simulation examples will be presented to demonstrate the new capabilities 

available in PISCES-2ET. The first two are for the application of carrier temperature analysis. These 

are simulations for the substrate current in MOSFET and output characteristics of SOI structures. Both 

simulated and measured data are compared. The last two are for the simulation of heterostructures. 

Among them the first one shows the electrical simulation of a GaAs/AlGaAs-based LED (for light 

emitting diode) with cylindrical symmetry. One unique feature of this example is the existence of the 

floating layer in the structure, which poses numerical difficulty. The second example for 

heterostructure analysis is the simulation of an AlInAs/GaInAs-based MODFET in which the surface 

Fermi-level pinning is shown. 

6.1 Substrate Current of MOS Structure 

This examples is to show the effect of the carrier-energy dependent impact ionization model 

on the substrate current of MOSFET. It has been known that the drift-diffusion (DD) model gives 

bigger-than-expected substrate current even for relatively long channel MOSFETs [22]. In this 

example, two MOS structures with effective channel length 2 and 0.8 µm, respectively, are simulated 

and the one with 0.8µm channel length is compared to the measured data. Following the approach in 

[42], the results are plotted in a format of log ( I sub ⁄ I d ) vs. 1 ⁄ ( V ds – V d, 

sat ) in which the 

experimental data are insensitive to the variations in the channel length, gate oxide thickness, and . 

V gs 



It can be clearly seen that the DUET model provides more reasonable results compared to the 

experimental data [42], [43] than does DD model. It should be noticed that during the simulation, one 

fitting parameter, which effectively changes the energy relaxation time (or equivalently the energy 

relaxation length) used in the expression for energy-dependent ionization rate, is used. The similar 

calibration approach has been reported in [22] too. The input deck to PISCES-2ET is listed below for 

this device structure. Special attention should be paid to the use of symbolic and model cards. In 

the symbolic card parameter engy.ele indicates that during the simulation the electron energy 

balance equation should also be solved together with the Poisson’s and carrier continuity equations. In 

the model card, three parameters are relevant to the energy-dependent impact ionization (II) model: 

imp.tn (but not with imp.tp) specifies that only electron energy dependent II model is used and 

for holes the impact ionization rate is still determined by the local field (a default). imp.jt indicates 

for energy-dependent II model, the current density rather than the saturation velocity is used to 

determine the II rate. Finally, impjt.rat is used to specify the ratio of L w 

to τ w v sat (refer to 

Eq. (3.39)). The simulation results are shown in Figure 6.2. 

title N-MOS for Substrate Current Simulation 

$ 

$ A 0.8 micron N-MOSFET example, Electron-ET model 

$ 

options plotdev=xterm x.scr=3.8 y.scr=3.8 

$ mesh 

$============================ 

mesh rect nx=40 ny=28 

x.m n=1 l=0 r=1 

x.m n=5 l=0.5 r=0.6 

x.m n=35 l=1.5 r=1.0 

x.m n=40 l=2.0 r=1.7 

y.m n=1 l=-0.0152 r=1 

y.m n=3 l=0.0 r=1 

y.m n=5 l=0.002 r=1 

y.m n=9 l=0.010 r=1 

y.m n=16 l=0.1 r=1 

y.m n=20 l=0.2 r=1 

y.m n=22 l=0.3 r=1 

y.m n=23 l=0.4 r=1 

y.m n=25 l=1.1 r=1 

y.m n=28 l=2.0 r=1 

$ region and electrodes 

$============================ 

region num=1 ix.l=1 ix.h=40 iy.l=1 iy.h=3 oxide 

region num=2 ix.l=1 ix.h=40 iy.l=3 iy.h=28 silicon 



$ Electrode: 1-Source, 2-Gate, 3-Drain, 4-Substrate 

elec num=1 ix.l=1 ix.h=4 iy.l=3 iy.h=3 




$ doping 

$============================ 

dop uniform p.type conc=2e17 reg=2 

dop gauss n.type conc=5e19 char=0.08 ra=0.7 x.r=0.52 y.t=0 y.b=0.10 dir=y 

dop gauss n.type conc=5e19 char=0.08 ra=0.7 x.l=1.48 y.t=0 y.b=0.10 dir=y 

$ contact 

$============================ 

contact all neutral 

contact num=2 workfunction=4.17 

$ initial solution 

$============================ 

symbolic newton carrier=0 

method itlim=50 p.tol=1e-5 c.tol=1e-5 

model srh fldmob conmob 

solve ini 

$ ramping vg and vd 

$============================ 

symbolic newton carrier=2 engy.ele 

model srh fldmob conmob imp.tn imp.jt impjt.rat=0.69 

method itlim=20 p.tol=1e-5 c.tol=1e-5 trap 

log ivfile=08_Tn.iv 

solve v2=0.2 vstep=0.2 nstep=3 electr=2 proj 

solve v2=1.0 outfile=08_Tn.g1 proj 



solve v3=3.0 outfile=08_Tn.g3 proj 

end 

Figure 6.1 Input file for simulation of the substrate current for MOSFETs. 



10 -1 

10 -2 

10 -3 

I 

sub /I d 

10 -4 

10 -5 

MIT 

Berkerley 

0.8 µm 

2 µm 

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 

1/(V ds 

- V dsat 

) 

Figure 6.2 Simulation results for the substrate current in MOSFET with 

two different channel length (2 and 0.8 µ m) and the 

comparison is made for 0.8 µ m case between the ET-simulated 

and measured results [42], [43]. The upper curves are 

simulated using DD model while the lower curves are obtained 

6.2 SOI Simulation 

This example shows simulation for SOI structures with two different channel length: 0.47 and 0.12 µm 

[44]. Input deck for the simulation of SOI with 0.12µm channel length is as follows: 

title SOI BERKELEY 

$ 

$ Effective channel length =.12um 



$ 0.12um of silicon on 0.4um oxide substrate 

$ 

$*************** define the rectangular grid ***********$ 

$ 

mesh outf=s/msh12r width=9.5 rect nx=43 ny=35 

$ 

x.m n=1 l=0.0 r=1.00 

x.m n=7 l=0.5 r=0.9 

X.m n=12 l=0.6 r=.9 

x.m n=22 l=0.74 r=1.15 

x.m n=32 l=0.88 r=0.85 

x.m n=37 l=0.98 r=1.1 

x.m n=43 l=1.48 r=1.1 

$ 

y.m n=1 l=0.0 r=1.00 

y.m n=6 l=0.4 r=0.80 

y.m n=21 l=0.46 r=1.15 

y.m n=33 l=0.52 r=0.80 

y.m n=35 l=0.54 r=1.00 

$ 




$ 

$*********** define the electrodes ************ 

$ #1-GATE #2-SOURCE #3-DRAIN #4-SUBSTRATE (below oxide) 

$ 

electrod num=1 ix.l=12 ix.h=32 iy.l=35 iy.h=35 




$ 

$*********** define the doping concentrations ***** 

$ 

doping uniform conc=6e16 p.type reg=2 

doping gauss conc=2e20 n.type characteristic=0.1 start=0.46 

+ x.right=0.6 ratio.lateral=0.25 region=2 


+ x.left=0.88 ratio.lateral=0.25 region=2 

$ 

interfac qf=20.e10 

contact num=1 n.poly 

plot.1d dop log abs a.x=0 a.y=0.4 b.x=1.48 b.y=0.4 min=14 max=21 

+ outf=s/dd/dop.12r ascii 



plot.1d dop log abs a.x=0 a.y=0.52 b.x=1.48 b.y=0.52 min=14 max=21 

$ 

models conmob intelmob print 

mobility ec.crit=8e4 char.int=0.04 

material region=2 vsaturation=1e7 

symb newton carriers=0 

$ 

method xnorm itlimit=30 

$ 

solve ini 

symb newton carriers=1 engy.ele 

method trap itlimit=30 

$ 

solve v1=-3 v4=-15 v3=2 vstep=0.5 nstep=10 electr=4 

solve v1=-3 v4=64 v3=0.05 

end 

The partial input deck for SOI with 0.4µm channel length is listed below. Only structural part 

is included. 

title SOI BERKELEY 

$ 

$ Effective Channel length =.47um 

$ 0.47um of silicon on 0.4um oxide substrate 

$ 

mesh width=9.5 rect nx=43 ny=35 

$ 

x.m n=1 l=0.00 r=1.00 

x.m n=7 l=0.5 r=0.9 

X.m n=12 l=0.6 r=.9 

x.m n=22 l=0.915 r=1.15 

x.m n=32 l=1.23 r=0.85 

x.m n=37 l=1.33 r=1.1 

x.m n=43 l=1.83 r=1.1 

$ 

y.m n=1 l=0.0 r=1.0 

y.m n=6 l=0.4 r=0.8 

y.m n=21 l=0.46 r=1.15 

y.m n=33 l=0.52 r=0.8 

y.m n=35 l=0.54 r=1.0 

$ 






$ 

$*********** define the electrodes ************ 

$ #1-GATE #2-SOURCE #3-DRAIN #4-SUBSTRATE(below oxide) 

$ 





$ 

$*********** define the doping concentrations ***** 

$ 

doping uniform conc=6e16 p.type reg=2 


+ x.right=0.6 ratio.lateral=0.25 region=2 


+ x.left=1.23 ratio.lateral=0.25 region=2 

$ 

interfac qf=20e10 

contact num=1 n.poly 

... 

end 

Figure 6.3 Input file for simulation of SOI structure. 

The simulation results are compared with the measured data provided by Hu’s group at UC 

Berkeley [44] in Figure 6.4. The agreement between ET model and experiment is good for devices with 

both channel lengths. While DD model gives good fit to the measured data for device with 0.47µ 

channel length, it grossly underestimates the drain current for device with 0.12 µ , an indication that 

DD models fails to predict the velocity overshoot phenomenon. 

6.3 Cylindrically Symmetric LED 

There are two unique features with the simulation of this light emitting diode (LED). The first is the 

cylindrical structure which requires the use of the cylindrical coordinate. PISCES-2ET has the 

capability of simulating cylindrically symmetric structure by specifying cylin in the mesh card. The 

second feature is the numerical difficulty caused by the existence of the current-blocking, floating n- 

layer in the p-region. To ensure the convergence of Newton iterations, a contact is put to the exterior 

perimeter of this floating layer and the zero-current boundary condition is applied. This technique 



guarantees the n-layer is indeed “floating” as far as the potential of the layer is concerned. The effect 

of the extra contact on the device characteristics is minor because the blocking layer is doped heavily. 

Following are two input files for the simulation. In order to put the contact to the floating layer from 

the exterior, the structure is shifted left in the lateral direction such that the rotation axis falls at x = 0 . 

For the initial solution, the voltage boundary condition is used first and then the zero-current boundary 

condition is switched on. It is observed that before the diode is turned on, i.e., for the bias below 1V, 

the numerical (discretization) noise may exceed the magnitude of the simulated current and so the 

current conservation law (the sum of the signed terminal currents should be zero) is not well observed. 

Because the device behavior before turning on is not a primary concern, bigger bias steps are used and 

especially the diode bias is increased directly from 0.7 to 1V. Also note that the n-layer is on the top 

of the structure, so the negative cathode bias is incremented. Figure 6.5 lists the first input file for the 

simulation for obtaining the initial solution with the voltage boundary condition. 

title Initial solution for LED starting from 0-carr 

$ 


$ 

0.006 

0.004 

I DS 

(A) 

L eff 

=0.12µ 

0.002 

L eff 

=0.47µ 

measured 

DD Model 

ET Model 

0.000 

0.0 0.5 1.0 1.5 2.0 

V DS 

(V) 

Figure 6.4 Simulated and measured data [44] for SOI structure 

with different channel length. 



$ ***** Define Rectangular Mesh ***** 

$ 

mesh rectangular nx=17 ny=29 cylin 

$ 

x.mesh n=1 l=-62.0 r=1.0 

x.mesh n=3 l=-37.0 r=1.0 

x.mesh n=5 l=-30.0 r=1.0 

x.mesh n=7 l=-13.0 r=1.0 

x.mesh n=9 l=-12.0 r=1.0 

x.mesh n=11 l=-11.0 r=1.0 

x.mesh n=13 l=-10.0 r=1.0 

x.mesh n=15 l=-9.0 r=1.0 

x.mesh n=17 l=00.0 r=1.0 

$ 

y.mesh n=1 l=0.000 r=1.0 

y.mesh n=5 l=1.000 r=1.0 

y.mesh n=9 l=3.600 r=1.0 

y.mesh n=13 l=4.600 r=1.0 

y.mesh n=17 l=5.600 r=1.0 

y.mesh n=21 l=7.600 r=1.0 

y.mesh n=25 l=8.900 r=1.0 

y.mesh n=29 l=40.00 r=1.0 

$ 

$ ***** Regions ***** 

$ 


region num=2 ix.l=1 ix.h=5 iy.l=1 iy.h=5 algaas xmole=0.00 



$ 

$ ***** Active Regions ***** 

$ 









$ 

$ ***** Electrodes ***** 

$ 






$ 

$ ***** Add Doping ***** 

$ 

dop unif conc=3e18 n.type x.l=-62.0 x.r=-30.0 y.t=0.0 y.b=1.0 


dop unif conc=2e18 n.type x.l=-10.0 x.r=0.0 y.t=3.6 y.b=4.6 



dop unif conc=1e18 p.type x.l=-62.0 x.r=-11.0 y.t=4.6 y.b=5.6 

dop unif conc=1e18 p.type x.l=-12.0 x.r=0.0 y.t=5.6 y.b=7.6 





$ 

$ ****** Plots ***** 

$ 

plot.2d boundary pause 

plot.2d grid pause 

$ 

$ ***** Contacts ***** 

$ 


symbol carrier=0 newton 

method itlim=50 p.tol=5.e-5 c.tol=5.e-5 

models temp=300 fldmob auger conmob rad consrh 

$ 

solve ini 


solve outfil=led.v0 

$ 

end 

Figure 6.5 

First input deck for the simulation of LED, used to find the initial solution for 

voltage boundary condition. 

The plots resulted from the running of the above file are shown in Figure 6.6 and Figure 6.7. 

Figure 6.6 shows the structure of the device and Figure 6.7 shows the mesh used in the simulation. 



Figure 6.6 

Device structure in terms of layers in LED. 

Figure 6.7 

Mesh used in the LED simulation. 

Once the initial solution is found with the voltage boundary condition, the current boundary condition 

is switched on for the contact to the floating layer in order to ensure it being “floating” (no current 

drawn at this terminal). This is implemented in the second file as listed in Figure 6.8. 



title LED Simulation Using 0-carr Solution 

$ 


$ 

$ ***** Define Rectangular Mesh ***** 

$ 

mesh rectangular nx=17 ny=29 cylin 

$ 

x.mesh n=1 l=-62.0 r=1.0 

x.mesh n=3 l=-37.0 r=1.0 

x.mesh n=5 l=-30.0 r=1.0 

x.mesh n=7 l=-13.0 r=1.0 

x.mesh n=9 l=-12.0 r=1.0 

x.mesh n=11 l=-11.0 r=1.0 

x.mesh n=13 l=-10.0 r=1.0 

x.mesh n=15 l=-9.0 r=1.0 

x.mesh n=17 l=00.0 r=1.0 

$ 

y.mesh n=1 l=0.000 r=1.0 

y.mesh n=5 l=1.000 r=1.0 

y.mesh n=9 l=3.600 r=1.0 

y.mesh n=13 l=4.600 r=1.0 

y.mesh n=17 l=5.600 r=1.0 

y.mesh n=21 l=7.600 r=1.0 

y.mesh n=25 l=8.900 r=1.0 

y.mesh n=29 l=40.00 r=1.0 

$ 

$ ***** Regions ***** 

$ 





$ 

$ ***** Active Regions ***** 

$ 











$ ***** Electrodes ***** 

$ 




$ 

$ ***** Add Doping ***** 

$ 












$ 

$ ** Current boundary condition is now switched on for contact 3 

$ 


contact num=3 curr 


method itlim=50 p.tol=5.e-5 c.tol=5.e-5 trap 

models temp=300 fldmob auger conmob rad consrh 

$ 

load infil=led.v0 

log ivfil=led.iv 

solve i3=0 outfil=led.i0 

solve v1=-0.1 vstep=-0.1 nstep=5 elect=1 

solve v1=-0.62 vstep=-0.02 nstep=3 elect=1 

solve v1=-0.7 

solve v1=-1.0 vstep=-0.1 nstep=10 elect=1 proj 

$ 

plot.1d x.a=v1 y.a=i1 abs log 

end 

Figure 6.8 

Second input file for LED simulation. The initial solution is obtained from the 

voltage boundary condition and is switched to the current boundary condition for 

the floating layer contact. The bias step jumps from – 0.7 to – 1V to avoid the 

numerical instability. 



Figure 6.9 Simulated I – V characteristics of LED. Notice that the bias is applied to the 

top of the structure (n-layer), so it is negative and the current computed below 

0.7V is due to the numerical noise. 

The numerical convergence behavior during simulation is excellent. The simulated I-V characteristics 

is shown in Figure 6.9. The bias ramp is applied to the cathode of the diode, so the magnitude of the 

bias increase is in the opposite direction to the x-axis. 

6.4 AlInAs/GaInAs MODFET 

This n-channel MODFET is constructed in a rectangular region with source, drain, and channel regions 

all formed in a narrow-bandgap (0.72eV) Ga 0.47 In 0.53 As material. The doping in the channel region is 

light ( 5×10 

15 

cm -3 ) and the channel conduction is through the spill-over of electrons from a heavilydoped 

( 4×10 

18 

cm -3 ), adjacent wide-bandgap (1.45eV) Al 0.48 In 0.52 As region. Because in PISCES- 

2ET ternary compound Ga x In 1-x As is represented by setting y = 1 in quaternary Ga x In 1-x As y P 1-y , in 

the input deck which follows “GaInAsP” is used instead of “GaInAs”. The gate contact is formed 

in a recessed manner. But in order to maintain the planarity of the structure, an oxide is filled in the 

recessed region. The structure is described in the following input file (Figure 6.10) and different 

regions in the device are plotted in Figure 6.11. 



title AlInAs/GaInAs based MODFET structure 

$ 

options plotdev=xterm x.screen=3.8 y.screen=3.8 

$ 

$ Rectangular mesh 

$ 

mesh nx=55 ny=30 rect 

$ 

x.mesh n=1 l=0.0 r=1.0 

x.mesh n=4 l=1.0 r=0.8 

x.mesh n=9 l=1.625 r=0.9 

x.mesh n=20 l=1.925 r=1.0 

x.mesh n=32 l=2.075 r=1.0 

x.mesh n=46 l=2.375 r=1.0 

x.mesh n=52 l=3.0 r=1.1 

x.mesh n=55 l=4.0 r=1.2 

$ 

y.mesh n=1 l=0.0 r=1.0 

y.mesh n=4 l=0.03 r=1.0 

y.mesh n=12 l=0.06 r=0.9 

y.mesh n=14 l=0.066 r=1.0 

y.mesh n=15 l=0.069 r=1.0 

y.mesh n=25 l=0.099 r=1.1 

y.mesh n=30 l=0.2 r=1.5 

$ 

$ Region and material specifications 

$ 

region num=1 ix.l=9 ix.h=46 iy.l=1 iy.h=4 insulator 

region num=2 ix.l=1 ix.h=9 iy.l=1 iy.h=4 gainasp 


region num=4 ix.l=1 ix.h=55 iy.l=4 iy.h=12 alinas 





$ 

$ Electrodes: 1 source, 2 gate, and 3 drain 

$ 




$ 

$ Doping specification 

xmole=0.47 ymole=1.0 


xmole=0.48 

xmole=0.48 

xmole=0.48 


xmole=0.48 



$ 

doping region=2 unif conc=2e19 n.type 







$ 

$ Background doping 

$ 

doping unif x.l=0.0 x.r=4.0 y.t=0.0 y.b=0.2 conc=5e14 p.type 

$ 

$ Interface trapping for the pinning of Fermi-level 

$ 

deepimp unif x.l=1.625 x.r=1.925 y.t=0.03 y.b=0.031 accep conc=1.0e19 

+ eion=0.7 

deepimp unif x.l=2.075 x.r=2.375 y.t=0.03 y.b=0.031 accep conc=1.0e19 

+ eion=0.7 

$ 

$ Show regions 

$ 

plot.2d bound pause 

$ 

$ Doping and x-mole profiles under the gate 

$ 

plot.1d dop x.s=2.0 x.e=2.0 y.s=0.0 y.e=0.2 log pause 

plot.1d xmol x.s=2.0 x.e=2.0 y.s=0.0 y.e=0.2 min=0.45 max=0.49 pause 

$ 

contact num=2 workf=4.8 surf.rec 

models temp=300 conmob consrh fldmob auger incompl 

$ 

$ Solving Poisson’s equation only for the equilibrium solution 

$ 

symb newton carriers=0 

method itlimit=50 biaspart 

$ 

solve ini 

$ 

$ Switch to full set of semiconductor equations 

$ 

symb newton carr=2 

$ 



$ Re-solve at the equilibrium and save solution 

$ 

solve outfil=modfet.ini 

log ivfil=modfet.iv 

$ 

$ Band diagram under the spacer between the gate and drain regions 

$ 

plot.1d band.c neg x.s=1.8 x.e=1.8 y.s=0.0 y.e=0.2 min=-1.5 max=0.5 

plot.1d band.v neg x.s=1.8 x.e=1.8 y.s=0.0 y.e=0.2 unch 

plot.1d qfn neg x.s=1.8 x.e=1.8 y.s=0.0 y.e=0.2 unch line=3 pause 

$ 

$ Apply the negative gate voltage and sweep Vd upto 5.0 

solve v2=-0.8 v3=0.0 vstep=0.2 nstep=4 elec=3 proj 

solve v3=1.3 proj 

solve v3=1.6 proj 

solve v3=2.0 vstep=1.0 nstep=3 elec=3 proj 

$ 

plot.1d x.a=v3 y.a=i3 

$ 

end 

Figure 6.10 Input file for the simulation of AlInAs/GaInAs MODFET. The surface Fermilevel 

pinning is modeled by specifying the high density of deep level impurities 

at the free surface. 

The simulation results are shown in the following figures. Figure 6.12 shows the band 

diagram at the thermal equilibrium for the Fermi-level pinning due to the high density of the surface 

traps and the situation without surface pinning. Finally the simulated drain current vs. the drain voltage 

at V GS = – 0.8V is shown in Figure 6.13. 



Figure 6.11 Regions in AlInAs/GaInAs MODFET structure. 

Figure 6.12 Band diagram along the line segment located at the spacer between the source 

and gate in the direction perpendicular to the surface of the MODFET. The 

effect of Fermi-level pinning due to the surface traps is shown by comparison 

to the free surface. 



V GS =-0.8V 

Figure 6.13 Simulated output I – Vcharacteristics at V GS = – 0.8V. 




APPENDIX A 

Fermi-Dirac Distribution 

and Heterostructures 

A.1 Effect of Fermi-Dirac Statistics 

Now we consider a more general case in DUET model, i.e., the quasi-thermal equilibrium distribution 

function, f 0 , used to form the complete distribution function in Eq. (2.1) is a Fermi-Dirac distribution. 

The Fermi-Dirac distribution function has the form of 

f 0 ( r, 

k) 

= 

2 

---------------------------------------------------------- 

(A.1) 

⎛ 

1 exp E( k) 

Fn r) 

⎞ 

+ ⎜---------------------------------- 

⎟ 

⎝ k B T n ( r) 

⎠ 

We need to transform the function to have the dependence on n, T n , and ε (the kinetic energy). This 

can be done in the following procedure. First with Eq. (A.1), one can show that from the definition of 

n (the carrier density) that 

⎛E Fn ( r) – E C ( r) 

⎞ 

n = N C ( T n , T L )F 1 ⁄ 2 ⎜------------------------------------ 

⎟ 

(A.2) 

⎝ k B T n ( r) 

⎠ 

where N C has the same expression as in section 2.1 and F 1 ⁄ 2 is the Fermi integral of order one half. 

The definition of Fermi integral as used in this manual will be given in APPENDIX B together with 

some other related properties. To have more concise notation, we define two symbols: 


Fermi-Dirac Distribution and Heterostructures 

E 

η Fn – E 

n = --------------------- C 

k B T n 

which is a function of n and T n as can be seen from Eq. (A.2), and 

(A.3) 

F 

γ n ( η n ) 1 ⁄ 2 ( η n ) 

= --------------------- 

(A.4) 

exp( η n ) 

Note that γ n is actually a measure of the carrier degeneracy, i.e., it is always smaller than unity but 

approaches the unity for non-degenerate case ( η n → – ∞ ). There are similar expressions for holes, but 

η p is expressed as 

E 

η V E Fp 

p 

= 

– 

--------------------- 

k B T p 

(A.5) 

We can now express the separation of the quasi-Fermi level and band edge using the carrier 

concentration as follows: 

⎛ 

exp E Fn – E C ⎞ n 

⎜--------------------- 

⎟ = ----------------------------------------- 

(A.6) 

⎝ k B T n ⎠ N C ( T n )γ n ( nT , n ) 

Note that throughout this document, we use n and T n as the fundamental variables. Substituting this 

expression in Eq. (A.1), we obtain an equivalent form of the Fermi-Dirac distribution as follows: 

f 0 ( nT , n , ε) 

= 

2 

----------------------------------------------------------------------------- 

N C ( T n )γ n ( nT , n ) ε 

1 + ----------------------------------------- exp⎛----------- 

⎞ 

n ⎝k B T n 

⎠ 

(A.7) 

The complete distribution function can then be constructed as 

⎛ h 

f ( r, 

k) f 0 ( n( r) , T n ( r)ε , ( k) 

) τ( r, 

k) 

------------k ∇ f (A.8) 

* 0 q h ∂ f 

------------ 0 ⎞ 

= 

– ⎜ ⋅ – ------- k ⋅ E 

* 

2πm n 2πm n 

∂ε n ⎟ 

⎝ 

⎠ 

We will further make several assumptions to simplify the above expression. First we assume the 

effective mass is constant, i.e. for parabolic band structure. Then the carrier velocity, v , is related to 

the wave vector, k , by the following expression:, 



v 

= 

h 

------------ k 

2πm * 

(A.9) 

and the kinetic energy can be written as 

m 

ε 

* v 2 

= ----------- = -----------------------k 2 

(A.10) 

2 22π ( ) 2 m * 

Furthermore, in heterostructures the electric field might be different for electrons and holes depending 

on the gradient of the respective band edge. For electrons, we have 

1 

E n = --∇E (A.11) 

q C 

We assume the relaxation time ( k -dependent τ ) can be simplified to depend on the kinetic energy 

only, i.e., τ( r, 

k) = τ( r, 

ε) 

. Eq. (A.8) can then be written as 

h 2 

∂ 

f ( rv , ) f 0 ( nT , n , ε) τ( r, 

ε) v ∇ f 0 q f 0 

= 

– ⎛ ⋅ – ------- v ⋅ E ⎞ 

⎝ ∂ε n ⎠ 

(A.12) 

Now we are ready to evaluate the carrier current and its relevant coefficients. By doing so, 

one may also find the exact definition for some commonly used physical parameters such as the 

mobility and diffusivity. The carrier current can be evaluated from the distribution function as follows: 

1 

j n – q∫vf ( r, 

k) 

------------- dk (A.13) 

( 2π) 3 x dk y dk z q v f ( rv , ) ⎛ 

m n 

----- ⎞ 3 = = – 

∫ 

dv 

⎝ h ⎠ x dv y dv z = – q∫v f ( rv , )d 3 v 

where we have used symbol d 3 v = ( m * ⁄ h) 3 dv x dv y dv z and the introduction of ( 2π) – 3 in the integral 

in k -space is due to the quantum mechanics consideration. It would be desirable to perform the above 

integral over ε if the integrand is the function of r and ε only. This can be done through the following 

transformation: 

* 

m n 

* 

⎛----- 

⎞ 3 dv 

⎝ h ⎠ ∫ x dv y dv z 

* 

2π( 2m n ) 3 ⁄ 2 

= ------------------------------ ε 1⁄ 2 

dε = 

h 3 

∫ 

1 

------ ( k B T n ) – 3 ⁄ 2 N C ε 1 ⁄ 2 

dε 

π 

∫ 

(A.14) 

It should be noticed that the first part of the right-hand-side (RHS) in Eq. (A.12) is even in k - 

space and the second part is odd in k -space, thus in the integral of Eq. (A.13) the first part of the 



distribution function will vanish (by multiplying v the even part becomes odd), and only the second 

(odd) part is used in the integration. The result is as follows: 

j n 

q τ( r, 

ε)vv ∇ f 0 d 3 v q 2 ∂ f 

τ( r, 

ε 0 

= 

⎛ 

∫ 

)------- vvd 3 v⎞ ∫ 

⋅ – 

⋅ E (A.15) 

⎝ ∂ε ⎠ n 

Note that vv should be understood as the tensor. It is easy to identify the second term on the RHS 

represents the drift component because it is proportional to the electric field. The first term is, however, 

not clear at this stage and we need to further find out the form of ∇ f 0 . We now proceed to find its 

expression. 

∂ f 0 ∂ f 

∇ f 0 

------- 0 

∂ f 0 ⎛ λ 

∇n + --------∇T 

∂n ∂T n k B T n 

------- n 3 

– ---- ∇n -- λ n ε 

+ ⎜ 

⎛ ----- – ----------- ⎟ 

⎞ ⎞ 

= = ⎜ 

n 

∂ε n 2T 2 ∇T n ⎟ 

⎝ ⎝ n k B T n 

⎠ ⎠ 

Thus Eq. (A.15) becomes 

(A.16) 

1 

j n q k B T n λ n 

-- d 3 ∂ f 

vτ( r, 

ε 0 

– )------- vv 

n∫ 

⋅ ∇n qn – q 1 ∂ε 

n -- d 3 ∂ f 

vτ( r, 

ε 0 

= 

+ 

∫ 

)------- vv ⋅ E 

∂ε n 

3 

qn -- 1 1 

----- k 

2T B T n λ n 

-- d 3 ∂ f 

vτ( r, 

ε 0 1 

– – 

)------- vv 

n n∫ 

----- 1 ∂ε T n n -- ∂ 

d3 vτ( r, 

ε)ε f 0 

+ 

– 

∫ 

------- vv ⋅ ∇T 

∂ε 

n 

(A.17) 

This seemly formidably complex expression can greatly be simplified by introducing some familiar 

coefficients through identification of origin of each term. 

A.2 General Relationship between Mobility, 

Diffusivity, and Thermal Diffusivity 

Furthermore, the tensor representation can be reduced to scalar under the constant effective mass 

assumption we have made. That is, 

8π 

∫ d3 vvv = 

3h 3 ∫ ε 3 2 

dε Î 

(A.18) 

where Î is the identity matrix. By realizing the relationship of Î ⋅∇ 

= ∇ and by comparing to the 

standard drift-diffusion expression of the carrier current, one can write the following compact form: 



j n = qD n ∇n + qnµ n E n + qnD T n ∇T n 

(A.19) 

where coefficients D , µ , and D T are named as diffusion constant (or diffusivity), mobility, and 

thermal diffusivity, respectively. Comparing Eq. (A.19) with Eq. (A.17), one obtains 

µ n q 1 8π 

--------- 2m * ∂ f 

n3h 3 n τ( r, 

ε 0 

= – 

∫ 

)------- ε 3 ⁄ 2 

dε 

∂ε 

(A.20) 

D n 

= 

k B T n 

-----------λ 

q n µ n 

(A.21) 

T 1 

D n 

----- 3 T n 2 --D 8π *1 ∂ f 

n 

------- 2m 

3h 3 n 

-- τ r ε 0 

= – + 

n∫ 

( , )------- ε 5 2 

dε 

∂ε 

(A.22) 

where Î is the identity matrix. It becomes immediately clear from Eq. (A.20) and Eq. (A.21) that we 

have arrived a generalized Einstein relationship between the mobility, µ , and diffusivity, D as 

follows: 

D k B T k 

--- -------- B T 

λ -------- F 1⁄ 2( η) 

= = --------------------- 

(A.23) 

µ q q F – 1 ⁄ 2 ( η) 

where all T , λ , and η are for the same carriers as in D and µ . The relationship of D T and µ is not so 

obvious at the first glance. But for the special case of Boltzmann statistics, i.e. for 

there exists a special relationship that 

f 0 ( nT , n , ε) 

n ε 

= ------ exp⎛–----------- 

⎞ 

N C 

⎝ k B T n 

⎠ 

(A.24) 

Then we obtain 

∂ f 

-------- 0 

n ∂ ∂ f 

-------- 0 

= ------- 

∂T n 

∂T n ∂n 

(A.25) 

Note that this simple relationship does not hold for general Fermi-Dirac statistics. 

D n 

T 

∂D = -------- n 

∂T n 

(A.26) 



Now we consider the specific form of the relaxation time, 

2ET implementation, we assume the following power dependence: 

τ( r, 

ε) 

. For the current PISCES- 

τ( r, 

ε) = α( r, 

T L )ε – ν 

(A.27) 

where ν ≥ 0 and α is the remaining part of τ which does not depend on the carrier kinetic energy. To 

be more specific, we have explicitly expressed the lattice temperature ( T L ) dependence. Also note that 

α doesn’t have the units of time. 

With the above power dependence of the relaxation time on energy, we can find more direct 

link between D T and µ . Notice that 

∞ 

ε – ν ∂ f 0 

∫ 

------- ε 3 ⁄ 2 

∂ε 

dε = 

∫ε 3⁄ 2– 

ν 

df = ( 3– 

2ν)Γ⎛ 3 

0 

2 -- – 

⎝ 

ν ⎞ F1 

⎠ 2 

0 

∞ 

0 

( )( k B T n ) 3 ⁄ 2 – ν 

⁄ – ν η n 

(A.28) 

where integral by parts has been used during the derivation and ν must be no bigger than 3/2 to insure 

that no singularity occurs. For the same reasoning, one obtains 

Thus it is clear that 

∞ 

ε – ν ∂ f 0 

∫ 

------- ε 5 ⁄ 2 

∂ε 

dε = ( 5 – 2ν)Γ⎛ 5 2 -- – 

⎝ 

ν ⎞ F3 

⎠ 2 

0 

( )( k B T n ) 5⁄ 

2– 

ν 

⁄ – ν η n 

(A.29) 

or 

T 

D 

------ n 

µ n 

= 

1 

----- 3 2 --k B T n 

-----------λ ⎛5 

q n -- – ν⎞ k B T n 

----------- F 3 ⁄ 2– 

– 

– 

---------------- 

ν 

⎝2 

⎠ q 

T n 

F 1⁄ 2– 

ν 

(A.30) 

D n 

T 

= 

k 

-- 

q 

⎛5 

-- – ν⎞ F 3 ⁄ 2– 

ν 3 

---------------- – --λ 

⎝2 

⎠ 2 n µ n 

F 1 ⁄ 2– 

ν 

(A.31) 

We now consider a more specific case, that is for the case where the acoustic phonon 

scattering is dominant, then p = 1 according to Stratton [1]. Furthermore, for nondegenerate cases, 

using property Eq. (B.5), the ratio of Fermi integrals with different orders all become the unity, hence 

D n 

T 

even becomes zero. That is to say, the gradient of the carrier temperature doesn’t contribute to the 

current flow. 



A.3 Heterostructures 

For heterostructures, the effective mass would be a function of the position also. In evaluating 

∇ f 0 , therefore, one needs to take into consideration the variation of the effective mass. This can be 

done by adding an extra term in Eq. (A.16) as follows: 

∂ f 0 ∂ f 

∇ f 0 

------- 0 ∂ f 0 * ∂ f 

= ∇n + --------∇T (A.32) 

∂n ∂T n 

-------- 0 λ 

+ ∇m 

* n k B T n 

------- n ⎛3 

– ---- ∇n -- λ n ε ⎞ 3 

⎜ ----- – ----------- ⎟ 

n ∂m n 

∂ε n 2T 2 ∇T n 

-- λ n * 

= 

+ + ----- ∇m 

⎝ n k B T n 

⎠ 2 * n 

m n 

The last term on RHS constitutes another driving force the carrier transport, but the difference from 

the previous two driving forces due to ∇n and ∇T n is that the effective mass is a structure parameter 

and does not change during the solution process, i.e., it is not a basic variable. We will later rearrange 

the terms in such a way that only true driving forces appear in the current expression. Before we 

proceed further, we look for other structure parameters. As discussed previously, for heterostructures 

the electric field which is a direct consequence of the gradient of potential might be different for 

electrons and holes. Similar to Eq. (A.11), the electric field for holes can be express as the gradient of 

the valence band edge: 

1 

E p = --∇E 

q V 

(A.33) 

But for the entire semiconductor region, there is one variable for electrostatic potential, ψ . 

So it is desirable to link both E C and E V to ψ . We define for heterostructure the electrostatic potential 

as 

E 

ψ = –--------- vac 

(A.34) 

q 

where E vac is the energy level for vacuum. The advantage of defining the potential this way is to 

warrant it is continuous and differentiable for the electric field has to be finite in magnitude. This is 

extremely important as in the heterostructure, the conventional definition of the potential as the 

intrinsic Fermi level 



E 

E C + E 

Fi ------------------- V 

kT (A.35) 

2 

L ln N C T L 

= – ------------------ 

( ) 

N V ( T L ) 

where T L is the lattice temperature and the densities of states for conduction and valence bands are 

evaluated at the lattice temperature, is not necessarily continuous. We can then relate the band edges 

to the potential using band structure parameters: electron affinity χ and bandgap E g as follows: 

E C 

= 

– qψ – χ 

(A.36) 

E V 

= 

– qψ – χ – E g 

(A.37) 

We are now ready to rewrite the current expressions for electrons and holes. Based on 

Eq. (A.32) and Eq. (A.15), one obtains for electrons: 

3 k B T n * 

j n = qD n ∇n+ 

qnµ ⎛ 

n F n – --λ 

2 n 

-----------∇lnm ⎞ 

⎝ q n + qnD T ⎠ n ∇T n 

qD n ∇n qnD T n ∇T n qnµ n ∇ψ nµ n ∇χ 3 2 --λ * 

= + – – ⎛ + n k B T n ∇lnm ⎞ 

⎝ 

n ⎠ 

(A.38) 

For holes, 

j p 

= 

– qD p ∇p qpD T 3 

* 

– p ∇T p – qpµ p ∇ψ – pµ p ∇χ ( + E g ) – --λ 

2 p k T p ∇lnm p 

B 

(A.39) 

The above expressions can greatly be simplified if the quasi-Fermi level instead of the carrier 

concentration is used as the driving force for the carrier transport. By introducing the kinetic energy 

ε( k) = E( k) – E C ( r) 

in Eq. (A.2), the Fermi-Dirac distribution function can be written as 

Thus 

f 0 ( r, 

k) 

= 

2 

--------------------------------------------------------- = 

⎛ 

1 exp E( k) 

Fn r) 

⎞ 

+ ⎜---------------------------------- 

⎟ 

⎝ k B T n ( r) 

⎠ 

2 

----------------------------------------------------------------------------- 

⎛ 

1 exp ε( k) 

+ E C ( r) 

r– E Fn ( r) 

⎞ 

+ ⎜------------------------------------------------------ 

⎟ 

⎝ k B T n ( ) ⎠ 

(A.40) 

∂ f 0 ⎛ ε( k) + E 

∇ f 0 ( r, 

k) 

------- C ( r) – E Fn ( r) 

⎞ 

= ⎜∇E ∂ε C – ∇E Fn – ------------------------------------------------------∇T 

T n ⎟ 

⎝ 

n 

⎠ 

Substituting the above expression into Eq. (A.15) and using Eq. (A.11), one obtains 

(A.41) 



j n = nµ n ∇E Fn + qnQ n ∇T n 

where the thermopower Q is defined as 

(A.42) 

T k B 

Q n = D n + ---- ⎛ 3 (A.43) 

q 2 --λ – η ⎞ n n µn 

⎝ ⎠ 

Note that the coefficient for the current component explicitly due to the carrier temperature gradient 

in Eq. (A.42) is different from that in Eq. (A.19). But for the isothermal case ( 

expressions are reduced to the standard drift-diffusion (DD) form. 

T n 

= const ), both 




APPENDIX B 

Mathematical Properties of 

Fermi Integral 

We first define the Fermi integral of order ν as used in this document: 

1 

F ν ( η) 

= -------------------- 

Γν ( + 1) 

∫ --------------------dx 

1 + e x – η 

where Γ is the Gamma function which is defined as 

x ν 

(B.1) 

and has the properties of 

∞ 

∫ 

Γν ( ) = x ν – 1 e – x dx 

0 

(B.2) 


Γ⎛ 1 ⎝2 -- ⎞ 

⎠ 

= 

π 

(B.3) 

Γν ( + 1) = νΓ( ν) for ν > 0 

(B.4) 

There are a few useful properties of Fermi integral, which are used in the program. We list two of them 

below: 


Mathematical Properties of Fermi Integral 


lim F ν ( η) 

= e η regardless value of ν 

η→ – ∞ 

d 

------ F 

dη ν ( η) = F ν – 1 ( η) 

From the above properties, one can derive two useful derivatives: 

(B.5) 

(B.6) 

∂ 

----- η 

∂n n ( nT , n ) = 

where λ n is the symbol of λ( η n ) with λ defined as 

λ 

---- n 

n 

(B.7) 

λ 

= 

F 1 ⁄ 2 η 

F – 1 ⁄ 2 η 

( ) 

--------------------- 

( ) 

(B.8) 

Another useful derivative is 

∂ 

----- γ 

∂n n ( nT , n ) 

= 

γ 

---- n 

( 1 – λ 

n n ) 

(B.9) 

For holes there are completely analogous formulas and are listed below: 

∂ 

-----η 

∂p p ( pT , p ) 

= 

λ 

----- p 

p 

(B.10) 

∂ 

-----γ 

∂p p ( pT , p ) 

γ 

---- p 

( 1 – λ 

p p ) 

Now we give the expressions for the derivative of η and γ w.r.t. the carrier temperature T . 

= 

(B.11) 

∂ 

--------η 

∂T n ( nT , n ) 

n 

= 

– 3 

-- 

1 2 T -----λ n 

n 

(B.12) 

∂ 

--------η 

∂T p ( pT , p ) 

p 

3 

= –-------λ 1 

2 p 

T p 

(B.13) 



∂ 

--------γ 

∂T n ( nT , n ) 

n 

= 

γ n 

T n 

3 

–--( 1 – λ 

2 n )----- 

(B.14) 

∂ 

--------γ 

∂T p ( pT , p ) 

p 

3 

-- ( 1 – λ 

2 p ) γ p 

= – ----- 

T p 

(B.15) 




APPENDIX C 

Formulations in Previous 

PISCES-II Versions 

Considering the limited access to the manuals and reports for the previous versions of PISCES II (i.e. 

PISCES-II User’s Manual (1984) [3] and PISCES-IIB Supplementary report (1985) [4]), we list in this 

Appendix those equations and expressions referred to in the User’s Manual but not discussed in this 

report. Users may find the similar ones in the previous PISCES II reports. 

A n 

** 

Surface recombination velocities for electrons and holes, and , are given by 

A p 

** 

where and are the effective Richardson constants (p. 389 in [18]) for electrons and holes. 

Incomplete ionization for shallow doping impurities: 

v sn 

A ** 

v n T 2 

sn = -------------- 

qN C 

(C.1) 

A ** 

v p T 2 

sp = -------------- 

qN V 

v sp 

+ 

N D 

N Ā 

N D 

( – ) ⁄ kT 

= -------------------------------------------- 

1 g D e E Fn E 

+ 

D 

N A 

( – ) ⁄ kT 

= -------------------------------------------- 

1 g A e E A E 

+ 

Fp 

(C.2) 


Formulations in Previous PISCES-II Versions 

where E D and E A are impurity energies, g A and g D are degeneracy factors for donors and acceptors, 

respectively. 

Surface mobility reduction factor, g surf . To model the low-field mobility along the oxidesemiconductor 

interface in a simple way, the following formula is used: 

where 0 < g surf ≤ 1. 

µ 0 surface 

, = g surf µ 0, 

bulk 

(C.3) 

Field-dependent barrier lowering model for Schottky contacts: 

q 

∆φ b = ----------E 1 ⁄ 2 + αE 

(C.4) 

4πε s 

where E is the magnitude of the electric field at the interface. Both lowering mechanisms, image force 

(the first term on RHS of Eq. (C.4)) and static dipole layer (second term), are considered in the above 

model. 


References 

[1] R. Stratton, “Semiconductor current-flow equations (diffusion and degeneracy),” IEEE Trans. 

Elec. Dev., Vol. ED-19, pp. 1288-1292, Dec. 1972. 

[2] E. C. Kan, D. Chen, U. Ravaioli, Z. Yu, and R. W. Dutton, “Formulation of macroscopic 

transport models for numerical simulation of semiconductor devices,” to be published in VLSI 

Design, Aug. 1994. 

[3] M. R. Pinto, C. S. Rafferty and R. W. Dutton, “PISCES-II - Poisson and Continuity Equation 

Solver,'' Stanford Electronics Laboratory Technical Report, Stanford University, September 

1984. 

[4] M. R. Pinto, C. S. Rafferty, H. R. Yeager, and R. W. Dutton, “PISCES-II - Supplementary 

report,'' Tech. Rep., Integrated Circuits Laboratory, Stanford University, 1985. 

[5] N. D. Arora, J. R. Hauser, and D. J. Roulston, “Electron and hole mobilities in silicon as a 

function of concentration and temperature,” IEEE Trans. Elec. Dev., Vol. ED-29, pp. 292-295, 

Feb. 1982. 

[6] Z. Yu et al., “Development of doping and temperature dependent mobility model in GaAs using 

a robust optimizer,” Private communication, July 1993. 

[7] J. M. Dorkel and Ph. Leturcq, “Carrier mobility in silicon semi-empirically related to 

temperature, doping and injection level,” Solid-State Elec., Vol. 24, no. 9, pp. 821-825, 1981. 

[8] C. Lombardi, S. Manzini, A. Saporito, and M. Vanzi, “A physically based mobility model for 

numerical simulation of non-planar devices,” IEEE CAD, Vol. 7, no. 11, pp. 1164-1171, Nov. 

1988. 

[9] J. T. Watt, Modeling The Performance of Liquid-Nitrogen Cooled CMOS VLSI, Ph.D. 

dissertation, Stanford University, May 1989. 

[10] A. G. Sabnis and J. T. Clemens, “Characterization of the electron mobility in the inverted 

Si surface,” IEDM Technical Digest, pp. 18-21, 1979. 

[11] H. Shin, A. F. Tasch, Jr., C. M. Maziar, and S. K. Banerjee, “A new approach to verify and 

derive a transverse field-dependent mobility model for electrons in MOS inversion layers,” 

IEEE Trans. Elec. Dev., Vol. 36, no. 6, pp. 1117-1124, June 1989. 

[12] S. Schwarz and S. Russek, “Semi-empirical equations for electron velocity in silicon: Part II-- 

MOS inversion layer,” IEEE Trans. Elec. Dev., vol. ED-30, pp. 1634-1639, Dec. 1983. 


[13] H. Shin, G. M. Yeric, A. F. Tasch and C. M. Maziar, “Physically-based models for effective 

mobility and local-field mobility of electrons in MOS inversion layers,” Solid State Elec., Vol. 

34, no. 6, pp. 545-552, 1991. 

[14] D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping 

and field,” Proc. IEEE, pp. 2192-2193, Dec. 1967. 

[15] J. J. Barnes, R. J. Lomax, and G. I. Haddad, “Finite-element simulation of GaAs MESFET’s 

with lateral doping profiles and submicron gates,” IEEE Trans. Elec. Dev., Vol. ED-23, 

Sept. 1976. 

[16] H. R. Yeager, “Circuit-simulation models for the high electron-mobility transistor,” Ph. D. 

Thesis, Stanford University, April 1989. 

[17] W. Haensch and M. Miura-Mattausch, “The hot-electron problem in small semiconductor 

devices,” J. Appl. Phys., Vol. 60, p. 650, 1986. 

[18] S. M. Sze, Physics of Semiconductor Devices, 1st ed., p. 62, John Wiley & Sons, New York, 

1969. 

[19] K. Hui, C. Hu, P. George, and P. K. Ko, “Impact ionization in GaAs MESFET’s”, IEEE Elec. 

Dev. Lett., vol. 11, no. 3, p. 113, Feb. 1991. 

[20] D. Ritter, R. A. Hamm, A. Feygenson, and M. B. Panish, “Anomalous electric field and 

temperature dependence of collector multiplication in InP/Ga 0.47 

In 0.53 

As heterojunction 

bipolar transistors,” Appl. Phys. Lett. 60 (25), p. 3150, 22 June 1992. 

[21] I. Watanabe, T. Torikai, K. Makita, K. Fukushima, and T. Uji, “Impact ionization rates in (100) 

Al 0.48 

In 0.52 

As,” IEEE Elec. Dev. Lett., vol. 11, no. 10, p. 437, Oct. 1990. 

[22] J. W. Slotboom, G. Streutker, M. J. v. Dort, P. H. Woerlee, A. Pruijmboom, and D. G. 

Gravestejn, “Non-local impact ionization in silicon devices,” IEDM Technical Digest, p. 127, 

1991. 

[23] PISCES-II code, version 1985. 

[24] S. M. Sze, Physics of Semiconductor Devices, 2nd ed., John Wiley & Sons, New York, 1981. 

[25] R. S. Muller and T. I. Kamins, Device Electronics for Integrated Circuits, John Wiley & Sons, 

New York, 1977. 

[26] Sadao Adachi, “Material parameters of In 1-x 

Ga x 

As y 

P 1-y 

and related binaries,” J. Appl. Phys. 53 

(12), Dec. 1982, pp. 8775-8792. 


[27] S. M. Sze, ed. High-Speed Semiconductor Devices, John Wiley & Sons, New York, 1990. 

[28] Landolt-Börnstein, New York: Springer-Verlag, Vol. 17a, 1982. 

[29] M. Neuberger, III-V Semiconducting Compounds, Handbook of Electronic Materials Vol. 2, 

IFI/PLENUM: New York, 1971. 

[30] D. V. Lang, et al., “Measurement of the band gap of Ge x 

Si 1-x 

/Si strained-layer 

heterostructures,” Appl. Phys. Lett. 47 (12), pp.1333-1335, Dec. 1985. 

[31] M P C M Krijn, “Heterojunction band offsets and effective masses in III-V quaternary alloys,” 

Semicond. Sci. Technol. 6 pp. 27-31, 1991. 

[32] S. W. Corzine, et al., “Optical gain in III-V bulk and quantum well semiconductors,” in 

Quantum Well Lasers, ed. P. S. Zory, Jr., Academic Press, 1993. 

[33] Z. Yu and R. W. Dutton, “SEDAN III – A generalized electronic material device analysis 

program,” Tech. Rep. Stanford University, 1985. 

[34] R. People, K. W. Wecht, K. Alavi, and A. Y. Cho, “Measurement of the conduction-band 

discontinuity of molecular beam epitaxial grown In 0.52 

Al 0.48 

As/In 0.53 

Ga 0.47 

As, N-n 

heterojunction by C-V profiling,” Appl. Phys. lett. 43 (1), pp. 118-120, July 1983. 

[35] S. W. Corzine, R. H. Yan, and L. A. Coldren, “Theoretical gain in strained InGaAs/AlGaAs 

quantum wells including valence-band mixing effects,” Appl. Phys. Lett., 57 (26), pp. 2835- 

2837, 24 Dec. 1990. 

[36] S. E. Laux, “Techniques for small-signal analysis of semiconductor devices,” IEEE Trans. Elec. 

Dev., Vol. ED-32, No. 10, pp. 2028-2037, 1985. 

[37] Z.-Y. Wang, K.-C. Wu, and R. W. Dutton, “An approach to construct pre-conditioning matrices 

for block iteration of linear equations,” IEEE Trans. CAD, Vol. 11, No. 11, pp. 1334-1343, 

1992. 

[38] R. W. Freund, RIACS Tech. Rep. 91.18, NASA Ames Res. Ctr., Sept. 1991. 

[39] R. W. Freund and N. M. Nachtigal, RIACS Tech. Rep. 90.51, NASA Ames Res. Ctr., Dec. 

1990. 

[40] K. Wu, Z. Yu, L. So, R.W. Dutton, and J. Sato-Iwanaga, “Robust and Efficient AC Analysis of 

High-speed Devices,” IEDM Technical Digest, pp. 935-938, San Francisco, Dec. 1992. 


[41] Z. Yu, R.W. Dutton, and M. Vanzi, “An extension to Newton method in device simulators -- on 

an efficient algorithm to evaluate small signal parameters and to predict initial guess,” IEEE 

Trans. CAD, Vol. CAD-6, no. 1, pp.41-45, Jan. 1987. 

[42] T. Y. Chan, P. K. Ko, and C. Hu, “A simple method to characterize substrate current in 

MOSFET’s,” IEEE Elec. Dev. Lett., Vol. 5, no. 12, pp. 505-507, Dec. 1984. 

[43] G. G. Shahidi, D. A. Antoniadis, and H. I. Smith, “Reduction of channel hot-electron-generated 

substrate current in sub-150-nm channel length Si MOSFET’s,” IEEE Elec. Dev. Lett., Vol. 9, 

no. 10, pp. 497-499, Oct. 1988. 

[44] Chenming Hu, Private communication, 1993. 

[45] C. R. Crowell and S. M. Sze, “Temperature dependence of avalanche multiplication in 

semiconductors,” Appl. Phys. Lett., 9, pp. 242-244, 1966. 

[46] D. J. Rose and R. E. Bank, Global Approximate Newton Methods, Numerische Mathematik, 37, 

pp. 279-295, 1981. 

[47] R. Bank, W. M. Coughran, W. Fichtner, E. H. Grosse, D. J. Rose, and R. K. Smith, “Transient 

simulation of silicon devices and circuits,” IEEE Trans. Elec. Dev., pp. 1992-2007, Oct. 1985. 


User’s Manual 

CARD FORMAT 

PISCES-2ET takes its input from a user provided ASCII file. Each line is 

a particular statement (or card), identified by the first word on the card 

(i.e., card name). The remaining parts of the line are the parameters of that 

statement. The words on a line are separated by blanks or tabs. If more 

than one line of input is necessary for a particular statement, it may be 

continued on subsequent lines by placing a plus sign (+) as the first nonblank 

character on the continuation lines. Card and parameter names do 

not need to be typed in full; only enough characters to ensure unique 

identification is necessary. 

Parameters may be one of three types: numerical, logical, or character 

(string). Numerical parameters are assigned values by following the name 

of the parameter with an equal sign (=) and the value. Character parameters 

are assigned values by following the name of the parameter by an 

equal sign (=) and a string of characters. The first blank or tab delimits the 

string. The presence of a logical flag, which is represented by a character 


string, indicates TRUE while a logical flag preceded by a caret (^) indicates 

FALSE. 

In the card descriptions which follow, the letters required to identify a parameter 

(i.e. a word) are printed in upper case, and the remainder of the 

word in lower case. For each card, parameters are first presented in a SYN- 

TAX section and are then described in a PARAMETER section. 

CARD SEQUENCE 

The order of occurrence of cards is significant in some cases. Be aware of 

the following dependencies: 

• The MESH card must precede all other cards, except TITLE, 

COMMENT, and OPTIONS cards. 

• When defining a rectangular mesh, the order of specification is 

as follows: 

MESH 

X.MESH (all) 

Y.MESH (all) 

ELIMINATE 

SPREAD 

REGION 

ELECTRODE 

ELIMINATE and SPREAD cards are optional but if they occur 

they must be in that order. 

• DOPING cards must follow directly after the mesh definition. 

• Before a solution, a symbolic factorization is necessary. Unless 

solving for the equilibrium condition (initial solution), a 

previous solution must also be loaded to provide an initial 

guess. 

• Any CONTACT cards must precede the SYMBOLIC card. 

• Physical parameters may not be changed using the MATERIAL, 

CONTACT, or MODEL cards after the first SOLVE or LOAD 


card is encountered. The MATERIAL and CONTACT cards 

precede the MODEL card. 

• A PLOT.2D must precede a contour plot, to establish the plot 

bounds. 

• PLOT.2D, PLOT.1D, REGRID, or EXTRACT cards which 

access solution quantities (ψ, n, p, φ n , φ p , T n , T p , T L , current 

(density), recombination rate, etc.) must be preceded 

somewhere in the input deck by a LOAD or SOLVE card to 

provide those quantities. 

The execution of the program is line based, i.e. whenever a line is read in it 

is processed immediately. This feature allows users to run PISCES interactively. 

In the following, cards are described in an alphabetic order. 

CONVENTIONS 

Multiple choices of parameters are denoted by putting the parameters in 

the braces and separated them by vertical bars. Thus 

{ par1 | par2 } 

states that either par1 or par2 may be specified but not both. 

All file names are currently set to no more than 20 characters in length. 

Table M.1 lists the abbreviation of symbols for units in this manual. 

Table M.1 Abbreviation for units used in this manual. 

Abbr. 

K 

J 

s 

µ 

Units 

Kelvin 

Joule 

second 

micrometer 


Table M.1 Abbreviation for units used in this manual. 

A 

W 

C 

ampere 

watt 

coulomb 


CHECK 

COMMAND 

CHECK 

The CHECK card compares a specified solution (input) against the 

current solution, returning the maximum and average difference in 

electrostatic and quasi-Fermi potentials. The CHECK card is particularly 

useful for comparing solutions that have been obtained on different 

generations of regrids. Information for both solution and mesh is needed 

for check operation. All input files are assumed binary. 

SYNTAX 

CHeck 

file specification: 

Infile = Mesh = 

Samemesh = 

PARAMETERS 

Infile 

A character string specifying the name of the solution file to compare. 

(Default: null) 

Meshfile 

A character string as the name of the file containing the mesh for the 

solution specified by Infile. (Default: null) 


CHECK 

Samemesh 

A logical flag indicating that the solution in Infile used the same mesh as 

the current solution. (Default: false) 

EXAMPLES 

CHECK INFILE=file.sol MESH=file.msh 

Compare solution in “file.sol” obtained using mesh “file.msh” against the 

current solution. 


COMMENT 

COMMAND 

COMMENT 

The COMMENT card allows comments to be placed in the PISCES- 

2ET input file. The program ignores the information on the COMMENT 

card. 

SYNTAX 

COMment (or $) 

PARAMETERS 

None. 

EXAMPLES 

$ **** This is a comment - wow! **** 


CONTACT 

COMMAND 

CONTACT 

The CONTACT card defines the physical parameters of an electrode. If 

no CONTACT card is supplied for an electrode, it is assumed to be ohmic 

(charge-neutral and at the thermal equilibrium). Lumped elements, e.g., 

electrical (or thermal) resistor and capacitor, attached to the electrode are 

also specified here. See Section 2.3 for details. 

SYNTAX 

CONTAct 

+ 

number: 

{ NUmber = | ALL = } 

workfunction: 

{ NEutral = | ALUminum = | 

P.polysilicon = | N.polysilicon = | 

MOLybdenum = | TUNgsten = | 

MO.disilicide = | TU.disilicide = | 

Workfunction = } 

special conditions: 

Surf.rec = VSURFN = 

VSURFP = BArrierlow = 

{ ALPha = | CUrrent = | 

Resistance = | CApacitance = | 

COn.resist = | TH.resist = } 


CONTACT 

PARAMETERS 

ALL 

A logical flag to indicate the same properties defined in this card are to be 

applied to all electrodes. (Default: false) 

ALPha 

A real number for the linear, dipole barrier lowering coefficient ( α in 

Eq. (C.4)) in units of cm. (Default: 0.0) 

ALUminum 

A logical flag for using the work function of aluminum (4.17 eV). 

(Default: false) 

Barrierlow 

A logical flag to turn on the barrier lowering mechanism (Eq. (C.4)). 


CApacitance 

A real number for the capacitance per unit width (in z-direction) of a 

lumped capacitor to be attached to the contact, in units of F µ 

-1 . 

(Default: 0.0) 

COn.resist 

A real number for the distributed contact resistance, , in units of Ω cm 2 . 

The actual resistance associated with a certain area, A, of the contact is 

computed as R = ρ c ⁄ A. (Default: 0.0) 

CUrrent 

A logical flag to impose the current boundary condition. (Default: false) 

ρ c 


CONTACT 

MO.disilicide 

A logical flag for using the work function of molybdenum silicide 

(4.80 eV). (Default: false) 

MOLybdenum 

A logical flag for using the work function of molybdenum (4.53 eV). 


NEutral 

A logical flag to indicate that the work function is to be calculated from 

the doping level in the semiconductor at the contact assuming charge 

neutrality and thermal equilibrium. Note that neutral stands for charge 

neutral. (Default: true) 

N.polysilicon 

A logical flag for using the work function of silicon material, which is 

assumed to be the electron affinity for silicon (4.17 eV). (Default: false) 

n + Ω µ 

NUmber 

An integer for the electrode sequence number which must previously be 

defined in the ELEctrode card. (No default) 

Resistance 

A real number for the resistance per unit width (in the z-direction) of a 

lumped resistor to be attached to the contact, in units of . 


Surf.rec 

A logical flag to indicate that finite surface recombination velocities are to 

be used at the respective contact. (Default: false) 


CONTACT 

P.polysilicon 

A logical flag for using the work function of silicon material, which is 

assumed to be the sum of the electron affinity and bandgap of silicon 

(4.17 + E gap eV). (Default: false) 

p + µ 

TH.resist 

A real number for the thermal resistance, as defined in Eq. (2.28), per unit 

width (in z-direction) attached to the contact, in units of K s J -1 . 


TU.disilicide 

A logical flag for using the work function of tungsten silicide (4.80 eV). 


TUNgsten 

A logical flag for using the work function of tungsten (4.63 eV). 


VSURFN, VSURFP 

Real number parameters for electron and hole surface recombination 

velocities, respectively, in units of cm/s. (Defaults: as calculated according 

to Eq. (C.1)) 

Workfunction 

A real number for the work function to be used, in units of eV. (Default: 

using flag NEutral) 

If none of the special conditions above is specified, this contact is a normal 

ohmic (Dirichlet) boundary condition. 


CONTACT 

EXAMPLES 

CONTACT ALL NEUTRAL 

CONTACT NUM=2 ALUM SURF BARR 

Define all electrodes except number 2 to be neutral, and number 2 is 

aluminum. Besides a workfunction, electrode number 2 also includes 

finite surface recombination velocities and barrier lowering. Note that the 

definition on the second card overrides that of the first. 

CONTACT NUM=2 RESIS=1E5 

CONTACT NUM=4 CON.RES=1E-6 

Attach a lumped resistor to contact number 2 with a value of 10 5 Ω-µ. 

Include distributed contact resistance (10 -6 Ω-cm -2 ~ Aluminum) on 

contact 4. 


CONTOUR 

COMMAND 

CONTOUR 

The CONTOUR card plots contours on a two-dimensional area of the 

device, as specified by the most recent PLOT.2D card. So a PLOT.2D 

card must precede a CONTOUR card. 

If a quantity specified is a vector, the contour of its magnitude is plotted 

unless flag of either X.compon or Y.compon is specified in the same 

card. In that case, the corresponding component of the vector quantity is 

plotted. 

When a solution is loaded, model dependent quantities (e.g., current 

density and recombination) to be plotted are calculated with the models 

currently defined, not with the models that were defined when the solution 

was computed. This allows the display of, for instance, Auger and 

Shockley-Read-Hall components of recombination separately. For 

consistent value of the current density, the models used in the solution 

should be specified. The quantity to be plotted has no default. 

SYNTAX 

CONTOur 

+ 

plotted quantity: 

{ POtential = | QFN = | 

QFP = | VAlenc.b = | 

CONduc.b = | DOping = | 

ELectrons = | Holes = | 

NET.CHarge = | NET.CArrier = | 

J.Conduc = | J.Electr = | 


CONTOUR 

J.Hole = | J.Displa = | 

J.Total = | E.field = | 

Recomb = | Flowlines = | 

TEMP.Elec = | TEMP.Hole = | 

TEMP.Lat = | VELO.Elec = | 

VELO.Hole = | Impact = | 

GEN.Elec = | GEN.Hole = | 

ALPHAN = | ALPHAP = | 

E.field } 

range definition: 

MIn.value = 

DEl.value = 

MAx.value = 

NContours = 

control: 

LIne.type = 

ABsolute = LOgarithm = 

{ X.compon = | Y.compon = } 

PAuse = COLor = 

C1.color = C2.color = 





PARAMETERS 

ABsolute 

A logical flag to specify that the absolute value of the plotted quantity be 

taken. (Default: false) 


CONTOUR 

ALPHAN, ALPHAP 

Logical flags for impact ionization rates due to electrons and holes ( 

and in Eq. (3.37)), respectively. (Defaults: false) 

α p 

α n 

COLor 

A logical flag to specify that color fill, as opposed to simple lines, should 

be used to delineate contours. (Default: false) 

CONduc.b 

A logical flag for potential corresponding to the conduction band edge. 


C1.color, C2.color, ... , C9.color, C0.color 

Integer numbers to specify the color types for the contours. (Defaults: 

C1.color, 6; C2.color, 7; C3.color, 8; C4.color, 9; C5.color, 10; 

C6.color, 11; C7.color, 12; C8.color, 13; C9.color, 14; C0.color, 15) 

DEl.value 

A real number parameter to specify the interval between values of adjacent 

contours. (No default) 

DOping 

A logical flag for net doping concentration. (Default: false) 

E.field 

A logical flag for electric field. (Default: false) 

ELectrons 

A logical flag for electron concentration. (Default: false) 


CONTOUR 

Flowlines 

A logical flag for current flow lines. (Default: false) 

GEN.Elec, GEN.Hole 

Logical flags for impact ionization generation rates due to electrons and 

holes (first and second terms on the right hand side of Eq. (3.37)), 

respectively. (Defaults: false) 

Holes 

A logical flag for hole concentration. (Default: false) 

Impact 

A logical flag for generation rate due to impact ionization (G in Eq. 

(3.37)). (Default: false) 

J.Conduc, J.Displa, J.Electr, J.Hole, J.Total 

Logical flags for the conduction, displacement, electron, hole, and total 

current densities, respectively. (Default: false) 

LIne.type 

An integer parameter to define the type of plot line. (Default: 1) 

LOgarithm 

A logical flag for using logarithmic instead of original value of the 

quantity to plot. For rapidly varying quantities, the logarithmic value is 

often more revealing. Since many of the quantities may be negative, the 

program actually uses 

log( x) 

= sign( x) ⋅ log( 1 + x ) 

(M.1) 

to avoid overflow. To get the true logarithmic value of a quantity, use 

ABsolute and LOgarithm. The absolute value is then taken first and 

there is no danger of negative arguments. (Default: false) 


CONTOUR 

MIn.value, MAx.value 

Real number parameters to specify the minimum and maximum values of 

the quantity to be plotted, respectively. If the value is logarithmic, the 

minimum and maximum should be given as the logarithmic bounds. 

(Defaults: the actual minimum and maximum values of the quantity to be 

plotted over the device) 

NContours 

An integer parameter to specify the number of contours to be plotted. This 

is an alternative to the above specification. (No default) 

NET.CArrier 

A logical flag for net carrier concentration. (Default: false) 

NET.CHarge 

A logical flag for net charge density. (Default: false) 

PAuse 

A logical flag to cause the program to stop at the end of the plot so that a 

hard copy may be made before continuing. Execution can be resumed by 

hitting a carriage return. (Default: false) 

POtential 

A logical flag for electrostatic potential which is usually defined as the 

intrinsic Fermi level. (Default: false) 

QFN, QFP 

Logical flags for electron and hole quasi-Fermi levels, respectively. 

(Defaults: false) 

Recomb 

A logical flag for net recombination rate. (Default: false) 


CONTOUR 

TEMP.Elec, TEMP.Hole, TEMP.Lat 

Logical flags for electron, hole, and lattice temperatures, respectively. 


VAlenc.b 

A logical flag for potential corresponding to the valence band edge. 


VELO.Elec, VELO.Hole 

Logical flags for electron and hole velocities, which are derived from the 

carrier concentration and current density, respectively. (Defaults: false) 

X.compon, Y.compon 

Logical flags for taking x and y components of a vector quantity, 

respectively. (Default: false) 

EXAMPLES 

CONTOUR POTEN MIN=-1 MAX=3 DEL=.25 

Plots the contours of potential from -1 volts to 3 volts in steps of 0.25 

volts. 

CONTOUR DOPING MIN=10 MAX=20 DEL=1 LOG ABS 

In this example, the log of the doping concentration is plotted from 

10 

20 

1.0×10 to 1.0×10 

in steps of 10. By specifying ABsolute, both the n- 

type and p-type contours are shown. 

CONTOUR FLOW NCONT=11 

The current flow lines are plotted. The number of flow lines is 11 so that 

10% of the current flows between adjacent lines. 


DEEPIMPURITY 

COMMAND 

DEEPIMPURITY 

The DEEPIMPURITY card specifies the impurity doping with variable 

ionization energy. 

This card has essentially the same features as the DOping card except it 

allows users to specify the impurity ionization energy as well. Its main 

application is for trap DC analysis as shown in the example for MODFET 

simulation. 

SYNTAX 

DEepimpurity 

+ 

Doping card parameters: 

All parameters available in DOping card (see DOping) 

ionization energy 

Eioniz = 

PARAMETERS 

Eioniz 

Real number parameter to specify the ionization energy for (deep) 

impurity level, in units of eV. It is E C - E D for donors and E A - E V for 

holes. (Default: same as EDb and EAb in MAterial card) 


DEEPIMPURITY 

EXAMPLES 

DEEPIMP UNIF X.L=1.625 X.R=1.925 Y.T=0.03 

+ Y.B=0.031 ACCEP CONC=1.0e19 EION=0.7 

DEEPIMP UNIF X.L=2.075 X.R=2.375 Y.T=0.03 

+ Y.B=0.031 ACCEP CONC=1.0e19 EION=0.7 

This example shows how the DEEPIMPURITY card can be used to 

specify the surface traps. The traps have type of acceptors with ionization 

energy 0.7 eV (i.e., E A - E V = 0.7 eV, almost in the mid bandgap for 

GaAs). The trap density if viewed from per unit area would be 

19 

–4 12 

1×10 × ( 0.031 – 0.03) 

× 1×10 

= 1×10 

cm -2 . And the traps span in the 

x-direction from 1.625 to 1.925 µ and from 2.075 to 2.375 µ . 


DOPING 

COMMAND 

DOPING 

The DOPING card specifies the impurity doping in selected regions of the 

device. 

SYNTAX 

DOping 

 

profile type: 

{ Erfc = | Gaussian = | 

Uniform = | SUprem3 = | 

OLD.Suprem3 = | SImpldop = | 

S4geom = | AScii = } 

location: 

X.Left = 

Y.Top = 

X.Right = 

Y.Bottom = 

region: 

REgion = 

profile specification: 

If = Erfc or Gaussian: 

 

COncentrat = JUnction = 

J.Conc = SLice.lat = 

or 


DOPING 

DOSe = CHaracter = 

or 

COncentrat = CHaracter = 


{ N.type or DONor = | 

P.type or ACceptor = 

and any combination of 

RAtio.lat = Erfc.lat = 

Lat.char = PEak = 

DIrection = 

If = Uniform: 

COncentrat = 

{ N.type or DONor = | 

P.type or ACceptor = } 

If SUprem3 or OLD.Suprem3: 

 

Infile = 

 

Boron = PHosphor = 

ARsenic = ANtimony = 

The selected dopant file will be extracted from the 

SUPREM-III save file 

 

DIrection = STart = 

RAtio.lat = 


DOPING 

If 

= AScii: 

 

Infile = 

 

N.type or DONor = 

P.type or ACceptor = 

The ASCII concentrations in Infile are read and added 

to (N.type) or subtracted from (P.type) the impurity 

profiles. 

 

DIrection = STart = 

RAtio.lat = 

If = S4geom or SImpldop: 

save: 

Infile = 

Outfile = 

PARAMETERS 

ACceptor (P.type) 

A logical flag to specify p-type doping impurity (i.e. acceptors). 


AScii 

A logical flag for input doping file being in ASCII. If AScii is specified 

with SUprem3, then an ASCII SUPREM-III export file is expected. 


DOPING 

AScii without SUprem3 allows for input a simple ASCII data file 

containing information of concentration versus depth. The format of the 

ASCII input file is a depth in µ followed by a concentration in cm -3 -- one 

pair per line. By convention, positive concentrations refer to donors (ntype), 

while negative concentration values refer to acceptors (p-type). 


Boron, PHosphor, ARsenic, ANtimony 

Logical flags to indicate that the selected dopant profile will be extracted 

from the SUPREM-III save file specified by Infile. (Defaults: false) 

CHaracter 

A real number parameter for the principal characteristic length used in 

computing profiles specified by either Erfc or Gaussian, in units of µ. 

(No default) 

COncentrat 

A real number parameter for the peak doping concentration, in units of 

cm -3 . For a Uniform profile, it is the value of the doping level. (No 

default) 

DIrection 

A character of either x or y. Along with STart and RAtio.lat, it specifies 

where to locate a one-dimensional profile in the two-dimensional device 

and how to extend it to the second dimension. DIrection is the axis along 

which the profile is to be directed. (Default: y) 

DONor (N.type) 

A logical flag to specify 


n-type doping impurity (i.e. donors). 


DOPING 

DOSe 

A real number parameter for the total dose, in units of cm -2 . (No default) 

ERFC, Gaussian, Uniform 

Logical flags used to analytically describe profile shapes in either 

complementary error function (Erfc), or Gaussian (Gaussian), or 

constant (Uniform) form. Doping is introduced in the intersection of the 

location box and the region selected. The default box is set up to include 

the entire region. (Defaults: false) 

ERFC.lat 

A logical flag to specify ERFC doping distribution in the lateral direction. 


Infile 

A character string for the name of the input file from which the doping is 

either directly obtained or interpolated onto an existing mesh. If AScii is 

also specified, the doping profile specified in Infile is added to the 

previous, if any, impurity profile. (Default: null)Sc 

J.conc 

A real number parameter for the concentration at the junction, in units of 

cm -3 . (Default: COncentrat / 100) 

JUnction 

A real number parameter for the location of the junction, in units of µ. it 

must be located in semiconductor region, outside the constant doping box. 

When JUnction is used, the program computes the characteristic length 

by examining the doping at a point half way between the ends of the 

constant box and at the given depth. If some other lateral position is 

desired for the computation, use the parameter SLice.lat. (No default) 


DOPING 

Lat.char 

A real number for the characteristic length of the distribution in the lateral 

direction as opposed to that in the principal direction (CHaracter). (No 

default) 

OLd.Suprem3 

A logical flag to read the doping profile from the earlier version of 

SUPREM-III process simulation program. A binary structure file 

specified by Infile is read in. The defaults for the constant doping box are 

set up as a line, parallel to the surface, and located at STart. 


OUtfile 

A character string for the name of a binary file in which all the DOping 

cards in the present file will be saved. The first DOping card should have 

the OUtfile parameter, so that the doping information on it and all 

subsequent DOping cards are saved in that file. The file can be re-read 

after regridding to calculate the doping profile on a new mesh. 


PEak 

A real number parameter specifying the peak position of a doping profile, 

in units of µ. (Default: 0.) 

RAtio.lat 

A real number parameter governing the profile outside the constant doping 

box. The lateral profile is assumed to have the same form as the principal 

one, but is shrunk/expanded by the factor RAtio.lat. (Default: 0.8) 

REgion 

An integer parameter for the sequence number of the region where doping 

profile is to be added. This is an optional parameter. Multiple regions may 


DOPING 

be included by concatenating their region numbers into a single integer. 

(Default: all semiconductor region numbers concatenated) 

SImpldop 

A logical flag specifying use of the doping profile from a SIMPL-2 file 

(rectangular grid) to be interpolated onto an existing PISCES mesh. 

(default: false) 

SLice.lat 

A real number parameter, in units of µ, to specify the location in the lateral 

direction (as opposed to the principal one), at which the junction depth 

specified by JUnction is to be searched along the principal direction. (No 

default) 

STart 

A real number parameter to specify where a one-dimensional doping 

profile is to be located along the direction specified by DIrection, used 

together with RAtio.lat also. (Default: 0.0) 

SUprem3 

A logical flag to read the doping profile from the “export” file saved during 

a process simulation using the late release of SUPREM-III. The default 

is to read binary export files. If the AScii parameter is also specified, then 

ASCII SUPREM-III export files will be expected. The defaults for the 

constant doping box are set up as a line, parallel to the surface, and located 

at STart. (Default: false) 

S4geom 

A logical flag to read the doping profile from the “geometry” file saved 

during SUPREM-IV 2D process simulation. (Default: false) 


DOPING 

X.Left, X.Right, Y.Top, Y.Bottom 

Real number parameters to specify the x and y bounds of the constant 

doping box within the simulation region. Inside the box the doping level is 

constant. Outside this area it falls off along the principal axis according to 

the profile specifications and along the lateral axis according to the lateral 

parameters. (The default bounds of the box depend on the type and 

principal direction of the profile as shown in Table M.1. In the case of Erfc 

or Gaussian or Suprem3, the bounds are defaulted to a line perpendicular 

to the principal axis and located at the start (S) / peak (P) of the profile, 

respectively. This is denoted by the entry SP in the table.) 

Table M.1 Default bounding parameters for constant doping box. Uniform 

refers to the Uniform profile while x- and y-directions apply to one of 

Erfc, Gaussian, SUprem3, OLD.Suprem3, or AScii profiles when the 

principal direction is specified as such. 

Parameter 

X.Left 

X.Right 

Y.Top 

Y.Bottom 

Uniform 

Default 

All other profile type 

x - direction 

y - direction 

– ∞ 

SP 

– ∞ 

∞ 

X.Left 

∞ 

– ∞ 

– ∞ 

Y.Bot 

∞ 

∞ 

SP 

EXAMPLES 

DOP UNIF CONC=1E16 P.TYPE 

DOP GAUSS CONC=1E20 JUNC=0.85 N.TYPE PEAK=0 

A one-dimensional diode with substrate doping 10 16 cm -3 and Gaussian 

profile. 


DOPING 

DOP UNIF CONC=1E16 P.TYPE 

DOP GAUSS CONC=9E19 N.TYPE X.RIGHT=4 

+ JUNC=1.3 R.LAT=0.6 ERFC.LAT 

DOP GAUSS CONC=9E19 N.TYPE X.LEFT=12 

JUNC=1.3 R.LAT=0.6 ERFC.LAT 

An n-channel MOSFET with Gaussian source and drain. Because the 

default X.Right is +∞, for the source we must limit the constant part to 

X.Right = 4, and conversely for the drain. Thus the profile has a constant 

part along the surface, falls off as an error function towards the gate, and 

as a gaussian in the direction of the bulk. In both cases, the vertical 

junction is at 1.3 µm. 

COM *** SUBSTRATE *** 

DOP REGION=1 UNIF CONC=1E16 N.TYPE 

COM *** BASE *** 

DOP REGION=1 ASCII SUPREM BORON R.LAT=0.7 

+ INF=plt3.out1 START=0 

COM *** EMITTER *** 

DOP REGION=1 ASCII SUPREM PHOS R.LAT=0.8 

+ INF=plt3.out1 X.LEFT=12.0 X.RIGHT=13.0 

+ START=0 

Reads a SUPREM bipolar profile and add it to a uniform substrate 

concentration. Adds doping only to those points lying in region 1. 

COM *** SUBSTRATE *** 

DOP REGION=1 UNIFORM CONC=9.999463e+14 p.type 

COM *** EMITTER *** 

DOP REGION=1 ERFC N.TYPE CON=1e20 CHAR=0.1 

+ X.LEF=-1 X.RIG=0 R.LAT=0.8 

COM *** BASE *** 

DOP REGION=1 SUPREM3 INFILE=base.exp BORON 



DOPING 

COM *** COLLECTOR *** 

DOP REGION=1 GAUSS PHOS CON=1e17 CHAR=0.8 


Simulates a triple-diffused bipolar by using a mixture of analytic and 

SUPREM-III profiles. Uses an erfc for the emitter, a SUPREM-III profile 

for the base, a gaussian for the collector, and adding it to a uniform 

substrate concentration. Adds doping only to those points lying in 

region 1. 


ELECTRODE 

COMMAND 

ELECTRODE 

The ELECTRODE card specifies the location of electrodes including 

thermal contacts in a rectangular mesh. 

SYNTAX 

ELEctrode 

number: 

position: 

Number = 

{ IX.Low = IX.High = 

IY.Low = IY.High = | 

X.Low = X.High = 

Y.Low = Y.High = } 

Contact = | SURface = 

SUBstrate = | SYmmetri = 

type: 

Thermal = 

PARAMETERS 

Contact 

A logical flag for placing an electrode on the top of the surface of the 

semiconductor region (such as at the insulator-semiconductor interface) in 


ELECTRODE 

the device structure. If Y.Low is specified, the electrode has thickness of 

Y.Low extending to the semiconductor region. 

IX.Low, IX.High, IY.Low, IY.High 

Integer numbers to indicate that grids having x and y indices between 

IX.Low and IX.High and between IY.Low and IY.High, respectively, are 

designated electrode nodes. 

Number 

An integer number for the electrode. There may be up to ten electrodes, 

numbered 1, 2, 3, ... , 9, 0. They may be assigned in any order, but if there 

are N electrodes, none can have an electrode number above N. 

SUBstrate 

A logical flag for placing an electrode at the bottom of the semiconductor 

region in the device structure. If Y.Low is specified, then the electrode has 

thickness of Y.Low extending to the semiconductor region. 


SURface 

A logical flag for placing an electrode on the top (i.e., surface) of the 

device structure.(Default: false) 

SYmmetri 

A logical flag to place an electrode which is symmetric with the one 

specified in this card. The device must have a symmetric structure 


Thermal 

A logical flag to specify that the electrode is a thermal contact and there is 

no equal-potential requirement for those nodes on the same “electrode” 


ELECTRODE 

rather lattice temperature is required to be the same for those nodes. 

(Default: false, meaning normal electrode) 

X.Low, X.High, Y.Low, Y.High 

Real number parameters, in units of µ , to indicate that grids having x and 

y coordinates between X.Low and X.High and between Y.Low and 

Y.High, respectively, are designated electrode nodes. The function of 

these parameters is essentially the same as that of IX.Low, IX.High, 

IY.Low, and IY.High except that the grid location is identified by its real 

coordinates. (No defaults) 

EXAMPLES 

ELEC N=1 IX.LOW=1 IX.HIGH=40 IY.LOW=17 

+ IY.HIGH=17 

Define a typical back-side contact. 


ELIMINATE 

COMMAND 

ELIMINATE 

The ELIMINATE card terminates grids along lines in a rectangular mesh. 

SYNTAX 

ELIminate 

direction: 

range: 

X.direction = | Y.direction = 

IX.Low = 

IY.Low = 

IX.High = 

IY.High = 

PARAMETERS 


Integer parameters for indices of grids used to define a rectangular region 

where grids along every second line are removed. Successive eliminations 

of the same region remove grids following the same principle but are 

based on the most recent mesh. For horizontal elimination, the vertical 

bounds should be decreased by one at each re-elimination of the same 

region, and conversely for vertical eliminations. 

X.direction, Y.direction 

Logical parameters to determine whether to eliminate grids along vertical 

(Y.direction) or horizontal (X.direction) lines. One must be chosen. 


ELIMINATE 

EXAMPLES 

ELIM Y.DIR IY.LO=10 IY.HI=20 IX.LO=1 IX.HI=8 

ELIM Y.DIR IY.LO=10 IY.HI=20 IX.LO=1 IX.HI=7 

Points along vertical lines between 10 and 20 are removed except of those 

along line IX = 5. 


END (QUIT) 

COMMAND 

END (QUIT) 

The END card specifies the end of a set of PISCES input cards. The END 

card may be placed anywhere in the input deck; all input lines below the 

occurrence of the END card will be ignored. If an END card is not 

included, all cards in the input file are processed. 

SYNTAX 

ENd or Quit 

PARAMETERS 

None. 

EXAMPLES 

END 


EXTRACT 

COMMAND 

EXTRACT 

The EXTRACT card extracts integrated electrical quantities, such as net 

charge, over a selected region based on the solution. 

SYNTAX 

EXtract 

variable: 

NET.CHar = NET.CArr = 

Electron = Hole = 

Metal.charge = N.Resist = 

P.Resist = N.Current = 

P.Current = 

bounds: 

X.MIn = X.MAx = 

Y.MIn = Y.MAx = 

Contact = Regions = 

file i/o: 

Outfile = 

PARAMETERS 

Contact 

An integer as the number of the contact for which electrode quantities, e.g. 

current and (metal) charge, are integrated in its portion intersecting the 


EXTRACT 

bounded region designated by X.MIn, X.MAx, Y.MIn, Y.MAx. (No 

default) 

Metal.charge 

A logical flag to indicate that integrated charge on a contact or its portion 

is to be calculated. This flag is useful for studies such as capacitance. 


N.Current, P.Current 

Logical flags for computing electron and hole currents, respectively, 

through an electrode or its portion. (Defaults: false) 

NET.CHar, NET.CArr, Electron, Hole 

Logical flags for integrated net charge, net carriers, electron and hole 

concentrations, respectively, over a selected region in the device. 


N.Resist, P.Resist 

Logical flags for the resistance of a cross section due to electrons and 

holes, respectively. The resistance of a cross section is defined as the one 

for the resistor with unit thickness in the third dimension and using the 

cross section as contacts. That is (for electrons), 

1 

R n = --------------------- 

q nµ n ds 

∫ 

(M.2) 

where ∫ds 

for integration over the cross section, in units of Ω µ 

-1 . 


Outfile 

Character string for the name of an optional ASCII output file to which the 

result and bias information are to be written. (Default: null) 


EXTRACT 

Regions 

An integer to identify region(s) as defined in Region card. The 

integration will be conducted over only those nodes which fall within both 

the bounds specified by X.MIn, X.MAx, Y.MIn, Y.MAx and the particular 

set of regions specified by Regions. (No default) 

X.MIn, X.MAx, Y.MIn, Y.MAx 

Real numbers for the coordinates (in units of µ ) of bounds which define 

the rectangular region for the integration. (Default: the entire device) 

EXAMPLES 

EXTRACT P.RESIST 

Extracts the resistance of a p-type line diffused into a lightly doped n 

substrate. Since the p-conductivity of the substrate is negligible, the 

bounds of the integration can include the whole device. 

EXTRACT METAL.CH CONT=1 X.MIN=-2.0 X.MAX=2.0 

+ Y.MAX=-0.0499 Y.MIN=-0.0501 

The charge on the lower surface of a gate electrode is integrated. There is 

0.05 µm of gate oxide on the surface, which is at y = 0.0. 


IMPACT 

COMMAND 

IMPACT 

The IMPACT card specifies the impact ionization model used for (local) 

electric-field dependence. For many devices, the impact ionization model 

for continuity equations allows the accurate prediction of avalanche 

breakdown. The current models are for Si only. See also, relevant 

parameters in the MODELS and CONTOUR cards for both field and 

(carrier) energy dependent impact ionization models. 

The Newton method with 2-carrier must be specified on the METHOD 

card since impact ionization is a 2-carrier process. 

SYNTAX 

IMpact 

model: 

CRowell = MOnte = 

LAMDAE = LAMDAH = 

mode: 

Break = 

Ionpath = 

PARAMETERS 

Break 

A logical flag to calculate the breakdown voltage using the ionization 

integral. (Default: false) 


IMPACT 

Crowell 

A logical flag to use the analytical expression proposed by Crowell and 

Sze for temperature dependent impact ionization rates [45]. There are four 

parameters in this expression: ionization energy, ε i = 1.5E g 

, Raman 

optical phonon energy, ε r 

, carrier mean free path for optical phonon 

generation, λ, and the low temperature limit of the mean free path, λ 0 

. λ 

for electrons and holes can be altered by users through LAMDAE and 

LAMDAH in this card. The other parameters have values as used in [45]. 

If Crowell is not specified, the model as specified in Eq. (3.38) and 

Table 3.11 is used. (Default: false) 

Ionpath 

A logical flag to print the nodes, electric field, carrier ionization rates 

along the integration path for calculation of breakdown voltage. 


LAMDAE, LAMDAH 

Real number parameters for electron and hole mean free paths ( λ in [45]), 

–7 

respectively, in units of cm. (Default: LAMDAE = 6.2×10 

, LAMDAH = 

–7 

3.8×10 

at 300 K [45]) 

Monte 

Character string for the name of the output solution file from a Monte 

Carlo (MC) solver. A non-null string serves also as the flag to indicate that 

the impact ionization rates ( α ’s) are to be calculated from this MC 

solution file. (Default: null) 

EXAMPLES 

IMPACT CROWELL LAMDAE=6.2e-7 LAMDAH=3.8e-7 

Use the Crowell and Sze formulae with the default mean free paths. 


INCLUDE 

COMMAND 

INCLUDE 

The INCLUDE statement provides a shorthand way to include 

information from other files in the PISCES input file. The statements in 

the INCLUDEd file will be inserted into the PISCES input file in place of 

the INCLUDE statement when the input file is processed. The statements 

in the INCLUDEd file must use correct PISCES input syntax, and they 

must be in correct order with respect to the other statements in the present 

input file when the INCLUDEd file is expanded by the input parser. This 

is most useful for libraries of material and model parameters. 

SYNTAX 

INClude (SOUrce) 

filename: 

A character string 

PARAMETERS 

None. 

EXAMPLES 

INCLUDE MAT.ini 


INTERFACE 

COMMAND 

INTERFACE 

The INTERFACE card allows the specification of interface parameters 

(recombination velocities and fixed charges) at semiconductor-insulator 

boundaries. 

SYNTAX 

INTerface 

number: 

Number = 

parameters: 

S.N = 

Qf = 

S.P = 

location: 

X.MIn = 

Y.MIn = 

X.MAx = 

Y.MAx = 

PARAMETERS 

Number 

An integer for the sequence number of the interface. The maximum 

number is currently set to 10. (No default) 


INTERFACE 

Qf 

Real number for the interfacial fixed charge density, in units of cm -2 . 


S.N, S.P 

Real number parameters for electron and hole surface recombination 

velocities, respectively, at the semiconductor surface, in units of cm/s. 

(Defaults: 0.0) 


Real number parameters for the coordinates of bounds to define a 

rectangular region, in units of µ. Any oxide/semiconductor interfaces 

found within this region are applied with parameters specified in this card. 

(Default: entire device) 

EXAMPLES 

INTERFACE X.MIN=-4 X.MAX=4 Y.MIN=-0.5 Y.MAX=4 

+ QF=1E10 S.N=1E4 S.P=1E4 

Define an interface with both fixed charge and recombination velocities. 


LOAD 

COMMAND 

LOAD 

The LOAD card loads previous solutions from files for plotting or as 

initial guess for present solution at other bias point. 

SYNTAX 

LOAd 

solution files: 

INFile or IN1file = IN2file = 

Outdiff = Ascii = 

actions: 

Difference = 

Restore = 

No.check = 

PARAMETERS 

Ascii 

A logical flag to specify that any files read in or written to by Load should 

be ASCII rather than binary. (Default: false) 

Difference 

A logical flag to indicate that the difference between two solutions 

(IN1file and IN2file) is to be analyzed. The difference may be stored by 

specifying Outdiff and can only be used for the purpose of data plotting 

or extraction. (Default: false) 


LOAD 

INFile or IN1file, IN2file 

Character strings for file names. The INFile (or IN1file) and IN2file 

specify input files for solutions. INFile (or IN1file) and IN2file represent 

present and previous solutions, respectively. If only one solution is to be 

loaded (for plotting or initial guess requiring a single solution), INFile 

should be used. If two input files are needed to perform an extrapolation to 

obtain an initial guess (i.e., option Extrapolate on the SOLVE card), 

IN1file and IN2file should be used. The solution in IN2file is the first to 

be lost when new solution is obtained. (Defaults: null) 

No.check 

A logical flag to prevent PISCES from checking material parameter 

difference between the loaded file(s) and those specified in the current 

input file. Checking will never be done for loading of ASCII solution 

file(s). (Default: false) 

Outdiff 

Character string for name of file to which the difference from comparison 

of loaded solution files (flag Difference) is written to. (Default: null) 

Restore 

A logical flag to restore the material parameters and models in the loaded 

file as the current ones. (Default: false) 

EXAMPLES 

LOAD INF=SOL.IN 

Specifies that a single solution file called SOL.IN should be loaded. 


LOAD 

LOAD IN1F=SOL1.IN IN2F=SOL2.IN 

Two solutions are loaded. The present solution is to SOL1.IN and the 

previous solution is SOL2.IN. We intend to use SOL1.IN and SOL2.IN to 

project an initial guess for a third bias point. 

LOAD IN1F=SOL1.IN IN2F=SOL2.IN DIFF OUTD=SOL1-2 

Two solutions are loaded, and the difference calculated and stored in a 

third file. 


LOG 

COMMAND 

LOG 

The LOG card allows the I-V and/or AC characteristics of a run to be 

logged to ASCII file(s) specified by the user. Any I-V or AC data obtained 

subsequent to the card are saved. If a log file is already open, it is closed 

and a new file opened. 

The format of the data saved in AC log file is as follows. The first line in 

the file records the number of terminals for the device under simulation. 

The lines starting with “*” record the number of the activation terminal, 

the magnitude of the AC input signal (sinusoidal), frequency, and DC bias 

(terminal voltages if lumped external resistors exist). The lines without 

“*” record, in sequence, the number of the activation terminal, AC 

conductances, capacitances, and magnitude of admittances. 

SYNTAX 

LOG 

file specification: 

Ivfile or Outfile = 

Acfile = 

PARAMETERS 

Acfile 

Character string for the name of file to which the AC simulation results are 

to be written. (Default: null, meaning no AC data saved) 


LOG 

Ivfile or Outfile 

Character string for the name of file to which simulated I-V information is 

to written. (Default: null, meaning no DC data saved) 

EXAMPLES 

LOG IVFIL=out.iv ACFIL=out.ac 

Save the simulated I-V data in a file called out.iv and AC data in out.ac. 


MATERIAL 

COMMAND 

MATERIAL 

The MATERIAL card allows users to change default material parameters 

for the base semiconductor in the device (see Section 4.3.1 for explanation 

of base material). For the following three parameters: (static) dielectric 

constant, ε, thermal conductivity at room temperature, κ, and its 

temperature coefficient, α (in Eq. (3.36)), they can be changed from 

region to region using region number assigned in Region card. For 

default parameter value see Table 4.1. Some parameters which are not 

included in Table 4.1 are listed here for Si and GaAs (Table M.2 and 

Table M.3). 

SYNTAX 

MAterial 

region: 

{ NUmber = | Region = } 

material parameters: 

EG300 = EGAlpha = 

EGBeta = AFfinity = 

Permittivity = Vsat = 

MUN = MUP = 

G.surface = TAUN0 = 

TAUP0 = NSRHN = 

NSRHP = ETrap = 

AUGN = AUGP = 

NC300 = NV300 = 

ARICHN = ARICHP = 


MATERIAL 

GCb = GVb = 

EDb = EAb = 

KP.300 = KP.Alpha = 

PARAMETERS 

AFfinity 

Electron affinity, in eV. 

ARICHN, ARICHP 

Richardson constants for electrons and holes ( and in Eq. (C.1)), 

respectively, in units of A K -1 cm -2 . (Default: Table M.2). 

AUGN, AUGP 

Auger coefficients for electrons and holes ( and in Eq. (3.47)), 

respectively, in units of cm 6 s -1 . (Default: Table M.2) 

EAb, EDb 

Acceptor and donor ionization energies ( E A – E V 

and E C – E D 

in Eq. 

(C.2)), respectively, in units of eV. (Default: Table M.2) 

EGAlpha 

α in Eq. (4.2) of units eV K -1 . 

EGBeta 

β in Eq. (4.2) of units K. 

EG300 

Energy bandgap at 300 K (Eq. (4.2)), in eV. 

A n 

** 

c n 

A p 

** 

c p 


MATERIAL 

ETrap 

Trap level = E t -E i , in units of eV. (Default: Table M.2) 

GCb, GVb 

Degeneracy factors for the donor and acceptor levels ( and in 

Eq. (C.2)), respectively, unitless. (Default: Table M.2) 

G.surface 

Surface mobility reduction factor (g surf in Eq. (C.3)), unitless. (Default: 

Table M.2) 

KP.300 

Thermal conductivity at 300 K ( in Eq. (3.36)), in units of W cm -1 K -1 . 

κ 0 

(Default: Table 3.10) 

KP.Alpha 

Temperature coefficient for the thermal conductivity ( α in Eq. (3.36)), 

unitless. (Default: 1.2) 

MUN, MUP 

Low-field mobilities for electrons and holes, respectively, in cm 2 V -1 s -1 . 

NC300, NV300 

Effective densities of states for conduction and valence bands, 

respectively, at 300 K, in cm -3 . 

NSRHN, NSRHP 

Reference concentration in SRH recombination formula ( in 

Eq. (3.45)) for electrons and holes, respectively, in cm -3 . 

(Default: Table M.2) 

g D 

g A 

N SRH 


MATERIAL 

NUmber or Region 

An integer for the sequence number of the region where any of three 

material parameters: static dielectric constant (i.e. Permittivity), thermal 

conductivity at room temperature (KP.300) and its temperature coefficient 

(KP.Alpha) can be changed from region to region. Note that all other 

material parameters can only be changed for the entire device (base 

material). (No default) 

Permittivity 

Static dielectric constant, unitless. 

TAUN0, TAUP0 

Minority carrier lifetimes for electrons and holes as used in SRH formula 

( in Eq. (3.45)), in s. (Default: Table M.2) 

τ 0 

1.0 

Vsat 

Carrier saturation velocity, in cm/s. (Default: see Table 3.9 and Table 4.1) 

Table M.2 material parameters for Si and GaAs. 

Parameter Constant (units) Silicon GaAs 

G.surface Surface mob. reduction 1.0 1.0 

TAUN0 Electron lifetime (s) 

–7 

×10 1.0×10 

TAUP0 Hole lifetime (s) 

–7 

1.0×10 1.0×10 

NSRHN SRH ref. conc. in Eq. 

(3.45) for n (cm -3 ) 

16 

5.0×10 5.0×10 

NSRHP SRH ref. conc. in Eq. 

(3.45) for p (cm -3 ) 

16 

5.0×10 5.0×10 

ETrap Trap level (eV) 0.0 0.0 

AUGN Auger coeff. (n) (cm 6 /s) 

–31 

2.8×10 2.8×10 

AUGP Auger coeff. (p) (cm 6 /s) 

–32 

9.9×10 9.9×10 

–7 

–7 

16 

16 

–31 

–32 


MATERIAL 

Table M.2 material parameters for Si and GaAs. 

Parameter Constant (units) Silicon GaAs 

ARICHN 

Eff Richardson const (n) 

(A K -1 cm -2 ) 

110 6.2857 

ARICHP Eff Richardson const (p) 30 105 

(A K -1 cm -2 ) 

GCb Cond band degen factor 2.0 2.0 

GVb Val band degen factor 4.0 2.0 

EDb Donor energy level (eV) 0.044 0.005 

EAb Acceptor energy level (eV) 0.045 0.005 

Table M.3 Insulator permittivity 

Insulator Permittivity 

Silicon dioxide 3.9 

Silicon nitride 7.5 

Sapphire 12.0 

EXAMPLES 

MATERIAL TAUN0=5.0e-6 TAUP0=5.0e-6 MUN=3000 

+ MUP=500 

Defines SRH lifetimes and concentration-independent low-field mobilities 

for all the semiconductor regions within the device (all the other 

parameters are assumed to be their defaults, consistent with the 

semiconductor type chosen). 


MESH 

COMMAND 

MESH 

The MESH card either initiates the mesh generation phase or reads a 

previously generated mesh. 

SYNTAX 

MESh 

+ 

type: one of 

 

Infile = 

ASCII.In = 

 

Rectangular = 

NX = NY = 

Diag.flip = 

 

Geometry = Infile = 

Flip.y = SCale = 

output files: 

OUTFile = 

ASCII.Out = 

grid editor: 

OUT.Asc = 

SCale = 

Flip.y= 


MESH 

smoothing key: 

SMooth.key = 

dimension: 

CYLindrical = Width = 

electrodes: 

Elec.bot = 

Poly.elec 

PARAMETERS 

ASCII.In 

A logical flag to indicate that the input mesh file is an ASCII rather than a 

binary file. (Default: false) 

ASCII.Out 

A logical flag to indicate the mesh file, as specified by OUTFile, to be 

saved is an ASCII one. Otherwise it will be binary. (Default: false) 

Cylindrical 

This logical flag specifies that the mesh, whether generated in the current 

run or read in from a file, is to be rotated about the right edge of the 

rectangular simulation region to permit the simulation of cylindrically 

symmetrical devices. This information will not be written to the mesh file; 

it must be specified in the input deck for each PISCES run. (Default: false) 

Diag.flip 

A logical flag to flip the diagonals in a rectangular mesh about the center 

line of the mesh. If not set, all the diagonals will be in the same direction. 



MESH 

Elec.bot 

A logical flag to add an electrode to the bottom of the simulation region 

when the mesh file read in is a geometry file generated by a 2D process 

simulator such as SUPREM-IV. One of the possible applications of this 

flag is to add a substrate contact for a MOSFET structure. Currently, the 

electrode number assigned to this contact is hard-wired to 4 in the code. 


Flip.y 

A logical flag which reverses the sign of the y-coordinate. (Default: false) 

Geometry 

A logical flag to indicate that the input ASCII mesh file as specified by 

Infile was generated by either a 2D process simulator or by an external 

mesh generator. (Default: false) 

Infile 

The name of the previously generated mesh file. If flag ASCII.In is set, 

this file is an ASCII file. Otherwise, it is binary. If flag Geometry is set, 

this mesh file, which must be an ASCII one, was generated by either a 2D 

process simulator such as SUPREM-IV or by an external mesh generator. 


NX, NY 

Integer parameters for numbers of grids in the x- and y-directions for a 

rectangular mesh, respectively. (No defaults) 

OUT.ascii 

This logical flag indicates that an ASCII mesh file will be saved for later 

editing by an external grid editor. See Appendix B of [3] for details of the 

format. (Default: false) 


MESH 

OUTFile 

Specifies the name of the mesh file to be saved. The saved mesh file is 

either ASCII or binary depending on the flag ASCII.Out and can be read 

in by a later PISCES run. (Default: null) 

Poly.elec 

A logical flag to convert the region with material type of polysilicon to an 

electrode. The condition and application scope of this flag are the same as 

those of Elec.bot. Because of the potential difference in integer 

representation of the polysilicon region for different process simulators, 

this flag is not guaranteed to work properly but it has been tested using one 

of the commercial versions of SUPREM-IV. Currently the electrode 

number assigned to this contact is hard-wired to 3 in the code. (Default: 

false) 

Rectangular 

A logical flag which initiates the generation of a rectangular mesh. 

(Default: true) 

SCale 

An integer factor by which all the coordinates read in are multiplied. 

(Default: 1) 

SMooth.key 

This integer parameter causes mesh smoothing as described in Section 4.6 

of [3]. The digits of the integer are read in reverse order and decoded as 

follows: 

1. Triangle smoothing, maintaining all region boundaries fixed. 

2. Triangle smoothing, maintaining only material boundaries. 

3. Node averaging. 

Options 1 and 3 are the most common; 2 is used only if a device has 


MESH 

several regions of the same material and the border between the different 

regions is unimportant. (No default) 

Width 

This real number parameter specifies the width of the simulation region, 

i.e., the dimension in the z-direction, in units of microns. When this 

parameter is used, all units for currents become amperes instead of A/µ, 

otherwise simulated terminal currents are considered as current densities 

per micron in width. (Default: 1.0) 

EXAMPLES 

MESH RECTANGULAR NX=40 NY=17 OUTF=mesh1.msh 

Initiates a rectangular mesh with number of grids 40 in x-direction and 17 

in y-direction before possible grid elimination and requests the finished 

mesh to be stored in a (binary) file named mesh1.msh. 

MESH INF=mesh1.msh OUT.ASC=mesh1.msh FLIP 

+ ASCII.OUT 

Reads a previously generated (binary) mesh file and generates an ASCII 

file for a mesh editor (the y-axis is inverted as specified by flag FLIP 

because the grid editor obeys the convention that positive y is upward, 

while PISCES follows the semiconductor convention of positive y being 

into the bulk). 

MESH GEOM INF=geom1 SMOOTH.K=13131 

+ OUTF=mesh1.msh 

Reads an ASCII geometry file, smooths the mesh, and stores the file for a 

later run (ASCII format). The smoothing does several averaging and 

flipping steps. The digits are read in a reverse order, so that the flipping 

comes first, followed by node averaging, and so on. 


MESH 

MESH GEOM INF=mos.geom POLY.ELEC ELEC.BOT 

Reads in an ASCII geometry (mesh) file for a MOS structure generated by 

one of 2D process simulators, converts the polysilicon layer into the third 

contact (the first two are source and drain contacts), and add the fourth 

contact to the substrate. The numbering convention for contacts is 

currently hard-wired in the code. 


METHOD 

COMMAND 

METHOD 

The METHOD card sets parameters associated with the particular 

solution algorithm chosen on the SYMBOLIC card. There can be more 

than one METHOD card in a single simulation, so that parameters can be 

altered. The default values of the parameters are used on the first 

occurrence of the METHOD card; subsequent METHOD cards only alter 

those coefficients specified. 

SYNTAX 

METhod 

+ 

general parameters: 

ITlimit = Xnorm = 

C.toler = P.toler = 

T.toler = TL.toler = 

Rhsnorm = LImit= 

PRint = Fix.qf= 

Biasparti or TRap = ATrap = 

method-dependent parameters: 

 

(The following parameters are for damping the Poisson updates) 

{ DVlimit = | DAMPEd = } 

DElta = DAMPLoop = 

DFactor = 

(The following parameters select acceleration methods for the 


METHOD 

Gemmul iteration) 

SInglepois = ICcg= 

LUcrit or LU1crit = LU2crit = 

Maxinner = ACCElerat = 

ACCSTArt = ACCSTOp = 

ACCSTEp = 

 

AUtonr = NRcriter = 

2ndorder = TAuto = 

TOl.time = L2norm = 

Dt.min = Extrapolate = 

PARAMETERS 

ACCElerat, ACCSTArt, ACCSTOp, ACCSTEp 

These parameters deal with an acceleration method for attaining faster 

overall convergence in the single-Poisson mode (Carriers = 0 in 

SYmbolic card). The logical flag ACCElerat specifies that acceleration 

is to be used. ACCSTArt is the starting value of the acceleration 

parameter, ACCSTOp is the final (limiting) value of the acceleration 

parameter and ACCSTEp is the step to be added to the value of the 

acceleration parameter after each iteration [3]. (Defaults: ACCElerat, 

false; ACCSTArt, 0.3; ACCSTOp, 0.6; ACCSTEp, 0.04) 

AUtonr, Nrcriter 

These two parameters are for implementing an automated Newton- 

Richardson procedure which attempts to reduce the number of LU 

decompositions per bias point. The logical flag AUtonr indicates that this 

algorithm is to be used. Real number parameter Nrcriter is the ratio by 


METHOD 

which the norm from the previous Newton loop must go down in order to 

be able to use the same Jacobian (i.e., LU decomposition) for the current 

Newton loop. This is strongly recommended for full Newton iteration. 

(Defaults: AUtonr, false; Nrcriter, 0.1) 

Biasparti or TRap, ATrap 

Logical flag Biasparti (TRap) specifies that if a solution process starts to 

diverge, the electrode bias steps taken from the initial guess are reduced by 

the multiplicative factor ATrap, a real number. (Defaults: Biasparti, 

TRap, false; ATrap, 0.5) 

DAMPEd 

A logical flag to indicate the use of a more sophisticated damping scheme 

proposed by Bank and Rose [46] (this is the recommended option, 

particularly for large bias steps). (Default: false) 

DAMPLoop 

An integer for the maximum number of damping loops allowed to find a 

suitable damping coefficient. (Default: 10) 

DElta 

Real number parameter for the threshold value to determine the damping 

factor for ∆ψ, must be between 0 and 1. (Default: 0.5) 

DFactor 

Real number parameter for the factor which serves to increase the initial 

damping coefficient for the next Newton loop. (Default: 10.0) 

DT.min 

Real number parameter used in transient simulation for the minimum 

–25 

time-step allowed, in seconds. (Default: 1×10 

) 


METHOD 

DVlimit 

Real number parameter to limit the maximum update in ψ for a single 

loop, in units of the thermal voltage kT/q. (Default: 0.1) 

Extrapolate 

A logical flag used in transient simulation. Uses a second-order 

extrapolation to compute initial guess for the successive time-step. 


Fix.qf 

A logical flag to fix the quasi-Fermi potential of each non-solved for 

carrier to a single value, instead of picking a value based on local bias (see 

Section 5 of Chapter 2 [3] and the ‘‘P.bias'' and ‘‘N.bias'' parameters on 

the SOlve card). (Default: false) 

ICcg 

A logical flag to choose whether or not to use iteration to solve the multi- 

Poisson loops. It should be set whenever doing multi-Poisson. 


ITlimit 

An integer parameter for the maximum number of allowed outer loops 

(i.e., Newton loops or Gummel continuity iterations). (Default: 15) 

LImit 

A logical flag to indicate that the convergence criterion should be ignored, 

and iterations are to proceed until ITlimit is reached. (Default: false) 

LUCrit (LU1crit), LU2crit 

Real number parameters to specify how much work is to be done per 

Poisson loop (see Section 3 [3]) in Gummel sequential solution method 

(flag Gummel in SYmbolic card). The inner norm is required to 


METHOD 

decrease by at least LUcrit before returning, or to reach a factor of 

LU2crit below the projected Newton error, whichever is the smaller. (If 

the inner norm is allowed to exceed the projected Newton error, quadratic 

convergence is lost). (Default: LUCrit, LU1crit, 3×10 

; 

–2 

LU2crit, 3×10 

) 

L2norm 

A logical flag to indicate use of L2 norm in transient simulation. It 

specifies that the error norms be L2 as opposed to infinity norms for 

calculating the time-steps. (Default: true) 

Maxinner 

An integer to set the maximum number of ICCG iterations. (Default: 25) 

PRint 

A logical flag to print the terminal fluxes/currents after each continuity 

iteration; if this parameter is not set, the terminal fluxes/currents are only 

printed after the solution converges. (Default: false) 

P.toler, C.toler, T.toler, TL.toler 

Real number parameters for the termination criteria in iterations for 

solving the Poisson, carrier continuity, energy balance, and lattice thermal 

diffusion equations, respectively, unitless. (Defaults: 1×10 

) 

Rhsnorm 

A logical flag. If selected, the Poisson error is measured in C µ -1 and the 

continuity error in A µ -1 . P.toler then defaults to 1×10 

C µ -1 , and 

–18 

C.toler to 5×10 

A µ -1 . (Default: false) 

SInglepois 

A logical flag to indicate that only a single Poisson iteration is to be 

performed per Gummel loop as opposed to the default where the 

–5 

–26 

–3 


METHOD 

continuity equation is only solved after Poisson has fully converged. 


TAuto 

A logical flag used in transient simulation to force the program to select 

time-steps automatically from the local truncation error estimates. Note 

that automatic time-stepping is the default for the second-order 

discretization but is not allowed for the first-order scheme. (Default: true 

when flag 2ndorder set) 

TOl.time 

Real number parameter used in transient simulation for the maximum 

allowed local truncation error, unitless. (Default: 5×10 

) 

Xnorm 

A logical flag to indicate that the error norm in Poisson updates is 

measured in units of kT/q, and that in carrier updates is measured relative 

to the local carrier concentration. In this case the default value for both 

P.toler and C.toler is 1×10 

2ndorder 

–5 

. (Default: true) 

A logical flag used in transient simulation to specify that the second-order 

discretization of Bank, et al. [47] be used as opposed to the first-order 

backward difference method. (Default: true) 

–3 

EXAMPLES 

METHOD DAMPED P.TOL=1.e-30 RHSNORM 

+ XNORM=FALSE 

Specifies that for a simulation using the Gummel method (as previously 

specified by an appropriate symbolic card), damping is to be employed 


METHOD 

and the Poisson error tolerance should be 1×10 

C µ -1 . Note that because 

Xnorm defaults to true, Xnorm must be turned off to use the rhs norm as 

a convergence criterion. If Xnorm = false had not been specified, the rhs 

norm and the update norm would have both been printed, but only the 

update norm would have been used to determine convergence. 

METHOD TRAP ATRAP=0.5 

SOLVE INIT 

SOLVE V2=3 V3=5 OUTFILE=outa 

This example illustrates the TRap feature, which can be quite useful for 

capturing knees of IV curves for devices such as SCRs. The first SOLVE 

card solves for the initial, zero bias case. On the second SOLVE card, we 

attempt to solve for V2 = 3 volts V3 = 5 volts. If such a large bias change 

caused the solution algorithms to diverge for this bias point, the bias steps 

would be multiplied by ATrap (0.5); i.e., an intermediate point (V2 = 1.5 

volts, V3 = 2.5 volts) would be attempted before trying to obtain V2 = 3 

volts and V3 = 5 volts again. If the intermediate point can not be solved for 

either, PISCES-II will continue to reduce the bias step (the next would 

be V2 = 0.75 volts and V3 = 1.25 volts) up to 4 times. Note also that the 

intermediate solutions will be saved in output files in a manner similar to 

voltage stepping using the VStep parameter on the SOLVE card; i.e., if 

two intermediate steps to V2/V3 = 3/5 volts were required, they would be 

stored in “outa'' and “outb'' while V2/V3 = 3/5 volts would be stored in 

“outc”. 

METHOD TOL.TIME=1E-3 AUTONR 

This is an example of transient simulation. By default, the second-order 

discretization is used, but the required LTE, 1×10 

, is smaller than the 

default. Newton-Richardson is also used. Note that because the Jacobian is 

exact for the second part (BDF-2) of the composite time-step, there should 

be very few factorizations for the BDF-2 interval when AUtonr is 

specified (see chapter 2 of this report). 

–30 

–3 


MOBILITY 

COMMAND 

MOBILITY 

The MOBILITY card specifies the values for the parameters in the 

mobility models. 

SYNTAX 

MOBility 

carrier: 

HOle = 

region: 

BULk = 

numerical parameters: 

UMAx = UMIn = 

EXP1.tem = EXP.Conc = 

EXP2.tem = Ncrit = 

Vsat = EC.Crit = 

UConst = G.surface = 

CHar.int = Alpha = 

U0.unv = ETa = 

EC.Unv = Qss.conc = 

Int.off = DIst.epe = 

EXP.Eper = BNL = 

BPL = CNPre = 

CPPre = CNExp = 

CPExp = DELTAN = 

DELTAP = 


MOBILITY 

PARAMETERS 

Alpha 

Real number for the coefficient α in Intel’s local field dependent mobility 

model of transverse field reduction (Eq. (3.16)). (Defaults: 1.02 for 

electrons and 0.95 for holes) 

BNL, BPL 

Real number parameters for coefficient B in Eq. (3.18) (Lombardi’s 

mobility model) for electrons and holes, respectively. (Defaults: BNL, 

7 

4.75×10 ; BPL, 9.93×10 

) 

7 

BUlk 

A logical flag to indicate that parameters specified in the present card 

apply to the bulk as opposed to the surface mobility model. These 

parameters include: EXP1.tem, EXP.Conc, EXP2.tem, Ncrit, UMAx, 

and UMIn (Default: false, meaning that the surface mobility parameters 

are applied) 

CHar.int 

Real number parameter of λ in Eq. (3.5) to specify the decay length for 

the complementary error function used for the transition from bulk to 

surface mobility, in units of µ. (Default: 0.03) 

CNExp, CPExp 

Real number parameters for β in Eq. (3.18) (Lombardi’s mobility model) 

for electrons and holes, respectively. (Defaults: CNExp, 0.125 ; 

CPExp, 0.0317 ) 


MOBILITY 

CNPre, CPPre 

Real number parameters for α in Eq. (3.18) (Lombardi’s mobility model) 

for electrons and holes, respectively. (Defaults: CNPre, 1.74×10 

, 

CPPre, 8.84×10 

) 

DELTAN, DELTAP 

Real number parameters for δ in Eq. (3.18) (Lombardi’s mobility model) 

for electrons and holes, respectively. (Defaults: DELTAN, 5.82×10 

, 

DELTAP, 2.05×10 

) 

5 

14 

DIst.epe 

Real number parameter for the characteristic length L in computing the 

structure-dependent transverse field (Eq. (3.21)), in units of µ . 


EC.Crit 

Real number parameter for E crit 

in Eq. (3.15) (Intel’s local field mobility 

4 

4 

model), in units of V/cm. (Default: 4.2×10 for electrons and 3.0×10 

for 

holes) 

EC.Unv 

Real number parameter for E univ in Eq. (3.16) (Intel’s local field mobility 

model), in units of V/cm. (Defaults: 5.71×10 for electrons and 2.57×10 

for holes) 

ETa 

Real number coefficient for η in Eq. (3.22) of Watt’s surface mobility 

model. (Defaults: 0.5 for electrons and 0.33 for holes) 

EXP.Conc 

Real number parameter of c in Eq. (3.6) for analytical low-field mobility 

model. (Defaults: see Table 3.3) 

5 

5 

14 

5 


MOBILITY 

EXP.Eper 

Real number parameter of β in Eq. (3.15) for Intel’s local field mobility 

model (Section 3.1.2.1). (Defaults: 0.5) 

EXP1.tem 

Real number parameter of b in Eq. (3.6) for the analytical low-field 

mobility model. (Defaults: see Table 3.3) 

EXP2.tem 

Real number parameter of d in Eq. (3.6) for the analytical low-field 


G.surface 

Real number parameter of the reduction factor for the surface mobility 

with respect to the bulk one (g surf in Eq. (C.3)), unitless. (Default: 1.) 

Hole 

Logical parameter to indicate that the parameters specified in the present 

card apply to holes if their values are different for holes from electrons. 

These parameters include: EC.Unv, ETa, UCons, UMAx, and UMIn 

(Default: false, meaning that parameters apply to electrons) 

Int.off 

Real number parameter of d in Eq. (3.5) to specify the vertical offset from 

the Si/SiO 2 interface, in units of µ. (Default: 0.06) 

Ncrit 

Real number parameter of N 0 in Eq. (3.6) for the analytical low-field 

mobility model. (Defaults: see Table 3.3). 


MOBILITY 

Qss.conc 

Real number parameter of c in Eq. (3.7) to specify the conversion factor 

for converting q ss into equivalent impurity concentration for mobility 

reduction, in units of cm -1 . (Default: 1.0×10 

) 

UMAx, UMIn 

Real number parameters of µ max 

and µ min 

in Eq. (3.6) for analytical lowfield 


UConst 

Real number parameter of the low-field mobility for general 

semiconductor unknown to the program, in units of cm 2 V -1 s -1 . (No 

default) 

U0.unv 

Real number parameter of in Eq. (3.8) for Intel’s surface mobility 

model, in units of cm 2 V -1 s -1 . (Defaults: 783.5 for electrons and 247.4 for 

holes) 

7 

µ 0 

8 

Vsat 

Real number parameter for carrier saturation velocity. (Defaults: see 

Table 3.9) 

EXAMPLES 

MODELS conmob intelmob print 

MOBILITY ec.perp=8e4 char.int=0.04 

Using Intel’s structural mobility model for transverse field mobility 

reduction, with parameter of the critical field ×10 V/cm (default value: 

4 


MOBILITY 

4 

4.2×10 ) in Eq. (3.15) and characteristic length 0.04 µ (default value: 0.03) 

in Eq. (3.5). 


MODELS 

COMMAND 

MODELS 

The MODELS card sets the temperature for the simulation and specifies 

model flags to indicate the inclusion of various physical mechanisms and 

models. 

SYNTAX 

MODels 

model flags: 

{ SRH = | CONSrh = } 

AUger = BGn = 

CONMob = 

{ ANalytic = | ARora = | 

CCsmob = | User1 = } 

FLDmob = | 

{ ENgy.mob = | FMob.new = ) 

Hypertang = } 

TFldmob = 

{ SRFmob = | INTELMOB = 

INTELMOB.par = | STrfld = 

Lombardi = ) | OLdtfld = } 

{ IMPAct = | IMP.Jt = | 

IMP.NT = | IMP.NVt = } 

IMP.TN = IMP.TP = 

{ BOltzmann = | FErmidirac = } 

INComplete = PHotogen = 

PRint = 


MODELS 

numerical parameters: 

TEmperature = B.Electrons = 

B.Holes = E0= 

FLUx = ABs.coef = 

ACc.sf = INV.sf = 

OX.Left = OX.Right = 

OX.Bottom = TAU.WN = 

TAU.WP = II.AN= 

II.BN = II.CN= 

II.AP = II.BP = II.CP= 

PARAMETERS 

ABs.coef 

The optical absorption coefficient ( α in Eq. (3.43), Section 3.3.2) in units 

of cm -1 , used in photo-generation (flag PHotogen) modeling. 


ACc.sf 

The low-field mobility reduction factor for surface accumulation layers, 

used in conjunction with the non-local, transverse-field mobility model 

TFldmob (refer to [13] for details). (Default: 0.87) 

ANalytic 

A logical flag specifying an analytical doping and lattice-temperature 

dependent mobility model for silicon only (see Section 3.1.1.3). 



MODELS 

ARora 

A logical flag specifying an alternative doping and lattice-temperature 

dependent mobility model originally developed by Arora [5] for silicon 

and now is available for both silicon and GaAs [6] (see Section 3.1.1.4 for 

details). (Default: false) 

AUger 

A logical flag to specify the use of Auger recombination mechanism (Eq. 


B.Electrons, B.Holes 

Real number parameters used in the longitudinal field-dependent mobility 

reduction for silicon ( β in Eq. (3.30)). (Defaults: B.Electrons, 1.395; 

B.Holes, 1.215) 

BGn 

A logical flag for including band-gap narrowing mechanism. 


BOltzmann 

A logical flag for using Boltzmann carrier statistics. (Default: true) 

CCsmob 

A logical flag to invoke the mobility model of Dorkel and Leturcq for 

silicon [7], which includes carrier-carrier scattering effect, doping and 

lattice-temperature dependence (see Section 3.1.1.6). (Default: false) 

CONMob 

A logical flag to specify use of doping-dependent mobility. The default 

model is a table look-up for data in both silicon and GaAs at 300K. When 

used with other flags for doping dependent mobility such as ANalytic and 

CCsmob, the default model is overritten. (Default: false) 


MODELS 

CONSrh 

A logical flag to specify use of Shockley-Read-Hall recombination with 

doping-dependent carrier lifetimes (Eq. (3.45)). (Default: false). 

ENgy.mob 

A logical flag for using the carrier-temperature dependent mobility model 

as described in Section 3.1.3.3. Currently it applies to silicon only. 


E0 

A real number parameter used in the (longitudinal) field-dependent 

mobility model for GaAs ( in Eq. (3.31), Section 3.1.3.2). 

(Default: 4×10 

V/cm) 

3 

E 0 

FErmidirac 

A logical flag for using Fermi-Dirac carrier statistics. (Default: false) 

FLDmob 

A logical flag for considering the longitudinal field-dependent mobility 

reduction. The default model is Caughey-Thomas formulation [14] (Eq. 

(3.30)) for silicon and Thim’s model (with negative differential mobility) 

[15] (Eq. (3.31)) for GaAs. (Default: false) 

FLUx 

The incident photon flux at the y=0 surface (F ph in Eq. (3.43), 

Section 3.3.2) in units of photons/cm 2 . (Real number, default: 0.0) 

FMob.new 

A logical flag for use of a longitudinal field-dependent mobility model 

which is derived from the carrier-temperature dependent model (flag 


MODELS 

ENgy.mob) by field-temperature (of carriers) mapping. See Eq. (3.35) 

for the formulation. It applies to silicon only. (Default: false) 

Hypertang 

A logical flag to use hyperbolic tangent form for electron mobility in 

GaAs (Eq. (3.32)). This model avoids the negative differential mobility as 

exhibited in Thim’s model [15], thus improving the numerical stability. 


II.AN, II.BN, II.CN; II.AP, II.BP, II.CP 

Real number parameters used in the carrier-temperature dependent impact 

ionization model (Eq. (3.42), flagged by IMP.NT). (For defaults see 

Table 3.13) 

IIV.AN, IIV.BN; IIV.AP, IIV.BP 

Real number parameters used in carrier-temperature dependent impact 

ionization model (Eq. (3.41), flagged by IMP.NVt). (For defaults see 

Table 3.12) 

IMPAct 

A logical flag to include the impact ionization as part of the carrier 

generation term in the solution process. The default impact ionization 

model is the local field-dependent one (Eqs. (3.37)-(3.38)), and the model 

parameters can be changed through IMPACT card. This default model can 

be overwritten by one of the following flags: IMP.Engy (IMP.NT), 

IMP.NVt, and IMP.JT. (Default: false) 

IMP.Engy 

A logical flag to indicate that the carrier energy (i.e. temperature) 

dependent impact ionization model is to be used as opposed to the local 

field dependent model (default of flag IMPAct). There are several carrier- 


MODELS 

energy dependent models available (see Section 3.3.1.2 for details) and the 

default one is invoked by flag IMP.NT. (Default: false) 

IMP.Jt 

A logical flag for using carrier-temperature dependent ionization rate (Eq. 

(3.39)) in the impact ionization model as described in Eqs. (3.37)-(3.38). 


IMPJt.ratio 

Real number parameter, γ , in Eq. (3.39). It can be used to change the 

energy relaxation length in the mapping between electric field and carrier 

temperature to fit the experimental data. (Default: 1.0) 

IMP.NT 

A logical flag for using carrier-temperature dependent ionization model as 

described in Eq. (3.42). The unique feature of this model is that the carrier 

drift velocity (or equivalently, the current density) does not play any role 

in the generation rate due to the impact ionization. (Default: false) 

IMP.NVt 

A logical flag for using carrier-temperature dependent impact ionization 

model in which the carrier (drift) velocity is approximated by the 

saturation velocity (Eq. (3.40)). (Default: false) 

IMP.TN 

A logical flag to indicate that carrier-temperature dependent impact 

ionization model is to apply to electrons, whereas the impact ionization 

model for holes can be either local-field (no flag IMP.TP) or temperature 

(flag IMP.TP set) dependent. (Default: false) 


MODELS 

IMP.TP 

A logical flag to indicate that carrier-temperature dependent impact 

ionization model is to apply to holes, whereas the impact ionization model 

for electrons can be either local-field (no flag IMP.TN) or temperature 

(flag IMP.TN set) dependent. (Default: false) 

INComplete 

A logical flag to Indicate that incomplete-ionization of impurities should 

be accounted for (Eq. (C.2)). (Default: false) 

INV.sf 

The low-field mobility reduction factor for surface inversion layer, used in 

conjunction with the non-local, transverse-field mobility model TFldmob 

(refer to [13] for details). (Default: 0.75) 

INTELMOB, INTELMOB.par 

Logical flags for using Intel’s local field dependent mobility models (Eqs. 

(3.15)-(3.16)). Mobility reduction due to both transverse and longitudinal 

fields are taken into consideration simultaneously. The difference between 

these two models is in the expression for transverse field reduction. 


Lombardi 

A logical flag to specify use of Lombardi local transverse filed dependent 

mobility model (Eq. (3.17), also see [8]). (Default: false) 

OLdtfld 

A logical flag to specify use of the earlier version of UT Austin’s non-local 

transverse field dependent mobility model (Eq. (3.24), see also [11]). 



MODELS 

OX.Left, OX.Right, OX.Bottom 

Real number parameters to define the location of the gate oxide region 

(left, right, and bottom edges) in conjunction with the use of UT Austin’s 

non-local mobility models (flags OLdfld and TFldmob). (No default 

values but initialized to 0.0) 

PHotogen 

A logical flag to specify the use of external photo-generation as part of the 

carrier generation term. Two model parameters: FLUx and ABs.coef 

must also be specified to use this model (Eq. (3.43)). (Default: false) 

PRint 

A logical flag to print the status of all models and a variety of coefficients 

and constants. (Default: false) 

SRFmob 

A logical flag to invoke Watt’s surface mobility model (Eqs. (3.22)- 


SRH 

A logical flag to specify the Shockley-Read-Hall recombination (Eq. 

(3.44)) with constant carrier lifetimes. (Default: true) 

STrfld 

A logical flag to specify that the surface transverse field is evaluated by the 

structure information (Eq. (3.21)) rather by definition (Eq. (3.20). This 

flag is usually used together with one of the transverse field dependent 

mobility models such as INTELMOB. (Default: false) 


MODELS 

TAU.WN, TAU.WP 

Real number parameters of carrier energy relaxation times for electrons 

and holes (Eq. (3.34) and Table 3.9), in units of ps (pico-second). 

(Defaults: tau.wn=0.42 and tau.wp=0.25) 

TEmperature 

Specifies the environment temperature, in units of Kelvin. (Default: 300) 

TFldmob 

A logical flag to invoke the second version (as opposed to flag OLdfld) of 

UT Austin’s non-local transverse field mobility model (Eq. (3.28), see also 

[13]). It is based on an extended version of the Schwarz-Russek 

formulation [12]. (Default: false) 

User1 

A logical flag to specify Arora’s (ARora) doping and lattice temperature 

dependent mobility model but with the user-definable parameters (refer to 

Section 3.1.1.5). (Default: false) 

EXAMPLES 

MODELS CONMOB SRH FERMI TEMP=290 

Selects concentration-dependent mobility and SRH recombination. Fermi- 

Dirac statistics are used, and the simulation is specified to be performed at 

290K. 

MODELS CONMOB SRH ENGY.MOB IMP.TN IMP.JT 

+ IMPJ.Rat=0.81 

Selects concentration-dependent mobility, SRH recombination and a 

carrier temperature-dependent mobility reduction model. An impact 


MODELS 

ionization model IMP.JT for the electron system is specified. The energy 

relaxation time ratio in computing impact ionization rate is set to be 0.81. 


OPTIONS 

COMMAND 

OPTIONS 

The OPTIONS card sets options for an entire run. 

SYNTAX 

Options 

run control: 

G.debug or Debug = N.debug = 

CPUStat = CPUFile = 

plot control: 

PLOTDevice or PLOTTer or Terminal= 

PLOTFile = 

X.Screen = Y.Screen= 

X.Offset = Y.Offset= 

PARAMETERS 

CPUFile 

Character string for the name of the file to log the CPU statistics during 

PISCES run. (Default: null) 

CPUStat 

A logical flag to indicate that CPU statistics during PISCES run is to be 

outputted to the file specified by CPUFile. (Default: false) 


OPTIONS 

G.debug (Debug), N.debug 

Logical flags to print debugging information to the standard output. 

G.debug (or Debug) prints general information, while N.debug 

outputs more specifically numerical parameters. (Defaults: false) 

PLOTDevice (PLOTTer, Terminal) 

A character string to specify the output plot device. If no device is given, a 

default (usually the user's graphics terminal) will be used. PISCES uses 

the PLOTCAP graphics package from Stanford for plotting purpose. Refer 

to the PLOTCAP document for further details. The full set of supported 

devices is contained in the PLOTCAP data base (an ASCII file). Table M.4 

list many of the common possibilities. 

Table M.4 Possibilites for supported PLOTCAP devices. 

hp2648 hp2623 hp9873 tek4107 

xterm sunview vt240 tek4010 

ditroff PSfile tplot gplot 

If PSfile is used, a PostScript file named print.ps will be generated for the 

plot and can later be printed to obtain a hard copy using laser printers. 

Plots will be scaled to the size of the specific device. Also note that on 

color graphics terminals, the different line types are implemented as 

different colors; on the black and white monitors they are implemented as 

dot and line patterns. (Default: login terminal) 

PLOTFile 

A character string for name of the output file which is generally defined by 

the plot device. For example, a graphics terminal will use the terminal as 

the output file. Printers may have the output file be a spooler. The graphics 

output file can explicitly be set by the PLOTFile command. All graphics 

output will then be routed to the given file. Note that the contents of the 


OPTIONS 

file will be in a format specific to the given device. (Default: device 

specific) 

X.Offset, Y.Offset 

Real number parameters, in units of inches, to indicate the x- and y-offsets 

from the bottom-left corner of the screen, respectively. (Defaults: 0.0) 

X.Screen, Y.Screen 

Real number parameters, in units of inches, for the physical width and 

height of the screen, respectively. They are set automatically, depending 

on the plot device. They, however, can be altered for special effects (split 

screen plots, for instance). (Defaults: device’s size) 

EXAMPLES 

OPTIONS PLOTDEV=tek4107 X.S=6 Y.S=5 X.Off=1 

+ Y.OFF=0.5 CPUSTAT 

This sets up a plot for a Tektronix terminal, using a small centered 

window. CPU information is also logged to the default file. 

OPTIONS PLOTDEV=lw PLOTFILE=plot.ps 

Here we set the plot device to the LaserWriter and save the output in a file 

called plot.ps. 


PLOT.1D 

COMMAND 

PLOT.1D 

The PLOT.1D card plots a specific quantity along a line segment through 

the device (mode A), or plots an I-V curve of data (mode B). In mode A, 

one of the solution variables is plotted versus distance into the device. For 

vector quantities, the magnitude is plotted. In mode B, terminal 

characteristics can be plotted against each other by choosing the value to 

be plotted on each axis. 

SYNTAX 

PLOT.1d 

+ 

segment definition: 

X.Start or A.X = 

X.End or B.X = 

Y.Start or A.Y = 

Y.End or B.Y = 


{ POTential = | QFN = | 

QFP = | DOping = | 

ELectrons = | Holes = | 

NET.CHarge = | NET.CArrier = | 

J.Conduc = | J.Electr = | 


J.Total = | E.field = | 

Recomb = | BAND.Val = | 

BAND.Con = | VAcuum = | 

VELO.Ele = | VELO.Hol = | 

XMole = | TEMP.Ele = | 


PLOT.1D 

or 

TEMP.Hol = | TEMP.Lat = | 

GEN.Elec = | GEN.Hole = | 

IMpact or II.gener = } 

X.Axis = Y.Axis = 

INFile = DAta = 

control: 

LOgarithm or Y.Log = X.Log = 

ABsolute = X.ABsolute = 

NO.Clear = NO.Axis = 

AScii = Unchanged = 

INTegral = NEGative = 

NO.Order = POInts = 

PAuse = LIne.type = 

MIn.value = MAx.value = 

X.MAx = X.MIn = 

X.Component = Y.Component = 

Spline = NSpline = 

OUTFile = 

PARAMETERS 

ABsolute, X.ABsolute 

Logical flags to indicate use of absolute values for quantities to be plotted 

in y- and x-axes, respectively. (Defaults: false) 

AScii 

Specifies that the output file will have an ascii format (the default binary 

format is for use with the Stanford dplot system). (Default: false) 


PLOT.1D 

BAND.Val 

A logical flag for plotting valence-band potential. (Default: false) 

BAND.Con 

A logical flag for plotting conduction-band potential. (Default: false) 

DAta 

Logical flag to indicate an HP measured I-V file will be used as an input 

file for plotting. (Default: false) 

DOping 

A logical flag for plotting doping. (Default: false) 

E.field 

A logical flag for plotting electric field. (Default: false) 

ELectrons 

A logical flag for plotting electron concentration. (Default: false) 

GEN.Elec, GEN.Hole 

Logical flags to plot the generation rates due to impact ionization caused 

by electron and hole currents, respectively. (Defaults: false) 

Holes 

A logical flag for plotting hole concentration. (Default: false) 

IMpact (II.gener) 

A logical flag for generation rate due to impact ionization (G in 

Eq. (3.37)). (Default: false) 


PLOT.1D 

INFile 

Character string for name of the input file in which the solution is stored. 


INTegral 

Plots the integral of the specified ordinate. (Default: false) 

J.Conduc, J.Electr, J.Hole, J.Displa, J.Total 

Logical flags to plot conductive, electron, hole, displacement, and total 

currents, respectively. (Defaults: false) 

LIne.type 

Specifies the line type for the plotted curve. (Default: 1) 

MIn.value, MAx.value 

Specify minimum and maximum values, respectively, for the ordinate of 

the graph. Default: found automatically from the data to be plotted. 

NEGative 

Negates the ordinate values. PISCES-II by default will order the plot 

coordinates by abscissa value; this ordering will result in unusual plots for 

IV curves with negative resistance, for example. (Default: false) 

NET.CArrier 

Plot net carrier concentration. (Default: false) 

NET.CHarge 

Plot net charge concentration. (Default: false) 

NO.Axis 

Indicates that the axes for the graph are not to be plotted. (Default: false) 


PLOT.1D 

NO.Clear 

Indicates that the screen is not to be cleared before the current plot so that 

several curves can be plotted on the same axis. (Default: false) 

NO.Order 

A logical flag to force PISCES to plot the data points as they naturally 

appear. (Default: false) 

Outfile 

Character string for name of an output file in which the data points plotted 

are to be put. If specified, the graphics output will be directed to that file. 

For further discussion, see the Options card. (Default: from Options 

card) 

PAuse 

Causes PISCES-II to stop at the end of the plot so that a hard copy may 

be made before continuing. Execution can be resumed by hitting a 

carriage return. (Default: false) 

POInts 

Marks the data points on the plotted curve. (Default: false) 

POTential 

Plot mid-gap potential. (Default: false) 

QFN, QFP 

Logical flags to plot electron and hole quasi-fermi levels, respectively. 


Recomb 

Plot net recombination. (Default: false) 


PLOT.1D 

Spline, NSpline 

The Spline option indicates that spline-smoothing should be performed on 

the data using NSpline interpolated points (maximum is 500). (Default: 

Spline, false; NSpline, 100) 

TEMP.Ele, TEMP.Hol, TEMP.Lat 

Logical flags to plot electron, hole, and lattice temperatures, respectively. 


Unchanged 

A synonym for NO.Axis and NO.Clear, but additionally it forces the use 

of the previous axis bounds so that a number of curves can easily be put on 

the same axis. (Default: false) 

VAcuum 

Logical flag to plot the vacuum energy level, a useful quantity for 

simulation of heterostructures because it is always continuous even at the 

abrupt material interface. (Default: false) 

VELO.Ele, VELO.Hol 

Logical flags to plot the electron and hole velocities, respectively. 


X.AXis, Y.Axis 

Character strings to indicate which quantities are to be used as x- and y- 

axes, respectively. 

In mode B, terminal characteristics can be plotted against each other by 

choosing the value to be plotted on each axis. Quantities available for 

plotting include applied biases (VA1, VA2,..., VA9, VA0), actual contact 

bias which may differ from applied bias in the case of lumped element 

boundary conditions (V1, V2, etc.), terminal current (I1, I2, etc.), AC 


PLOT.1D 

capacitances (C11, C12, C21, etc.), AC conductance (G11, G12, G21, 

etc.) and the magnitude of AC admittance (Y11, Y12, Y21, etc.). 

Additionally, any of the voltages or currents can be plotted versus time for 

transient simulations, and any AC quantity can be plotted versus 

frequency. The values plotted are the I-V or AC data of the present run, 

provided a log is being kept (see the LOG card). (Defaults: null) 

X.Component, Y.Component 

Logical flags to force the x or y components, respectively, of any vector 

quantities to be plotted, as opposed to the default magnitude. (Defaults: 

false) 

X.Log, Y.Log (LOgarithm) 

Logical flags for using logarithmic values of the quantities for plotting in 

x- and y-axes, respectively. 

For rapidly varying quantities, the use of logarithmic values is often more 

revealing. Since many of the quantities may become negative, PISCES 

actually uses the following expression 

log( x) 

= sign( x) ⋅ log 10 ( 1 + x ) 

(M.3) 

to avoid overflow. To get the true logarithm of a quantity, specify 

ABsolute and X.Log / Y.Log - the absolute is taken first and there is no 

danger of negative arguments. (Default: false) 

X.MAx, X.MIn 

Real number parameters to specify the maximum and minimum values for 

the abscissa to be plotted. (Defaults: the maximum and minimum abscissa 

values in the data to be plotted) 

XMole 

A logical flag to plot the mole fraction of a compound material. For 

quaternaries, only x nor y mole fraction is plotted. (Default: false) 


PLOT.1D 

X.Start, X.End, Y.Start, Y.End (A.X, B.X, A.Y, B.Y) 

Real number parameters to define the Cartesian coordinates of the start 

(X.Start, Y.Start or A.X, A.Y) and end (X.End, Y.End or B.X, B.Y) of 

a line segment along which the specified quantity is to be plotted. The data 

is plotted as a function of distance from the start (A). (The line segment 

may not be defaulted and it is required in mode A.) 

EXAMPLES 

PLOT.1D POTEN A.X=0 A.Y=0 B.X=5 B.Y=0 

Plots a graph of potential along a straight line from (0.0,0.0) to (5.0,0.0). 

PLOT.1D ELECT LOG A.X=1 A.Y=-.5 B.X=1 B.Y=8 

+ MIN=10 MAX=20 SPLINE NSPL=300 POINTS 

The log of the electron concentration is plotted from (1.0,-0.5) to (1.0,8.0) 

with bounds on the plotted electron concentration of 1.0e10 and 1.0e20. A 

spline interpolation is performed with 300 interpolated points. The nonspline-interpolated 

points are marked. 

PLOT.1D X.AXIS=V2 Y.AXIS=I1 

PLOT.1D X.AXIS=V2 Y.AXIS=I1 INF=logf0 UNCH 

The current in contact 1 is plotted as a function of contact 2 voltage, then 

the curve is compared with a previous run. 

PLOT.1D X.AXIS=V3 Y.AXIS=VA3 OUTFILE=save.plot 

Plots the actual contact voltage on a contact versus the applied voltage. 

PLOT.1D INFIL=FILE.AC X.AXIS=FREQ Y.AXIS=C21 

+ X.LOG 


PLOT.1D 

PLOT.1D INFIL=FILE.AC X.AXIS=FREQ Y.AXIS=C31 

+ X.LOG UNCH LINE=4 

This shows a plot of two capacitance components versus frequency saved 

in an AC log file from either a previous or present run. A different line 

type is chosen for the second component. 


PLOT.2D 

COMMAND 

PLOT.2D 

The PLOT.2D card plots quantities in a specified two-dimensional area of 

the device. A PLOT.2D card is also required before performing a contour 

plot (see CONTOUR card) in order to obtain the plot boundaries. 

SYNTAX 

PLOT.2d 

+ 

area definition: 

X.MIn = 

Y.MIn = 

X.MAx = 

Y.MAx = 


Grid or Mesh = Crosses = 

Boundary = Depl.edge = 

Junction = 

control: 

NO.TIc = NO.TOp = 

NO.Fill = NO.Clear = 

NO.Diag = LAbels = 

Flip.x = Pause = 

L.Elect = L.Deple = 

L.Junct = L.Bound = 

L.Grid = Outfile = 


PLOT.2D 

PARAMETERS 

Crosses 

A logical flag to plot crosses at the locations of grid points. (Default: false) 

Boundary 

A logical flag to indicate that the boundaries around the device and 

between regions are to be plotted. (Default: false) 

Depl.edge 

A logical flag to indicate that depletion edges are to be plotted. Note that 

depletion edges can only be plotted when a solution is present. (Default: 

false) 

Grid (Mesh) 

A logical flag to plot the grid including lines which delineate elements. 


Flip.x 

A logical flag to flip the plot about the y-axis; i.e., it negates all x 

coordinates so that the plot is mirrored. (Default: false) 

Junction 

A logical flag to specify that the junctions from the doping profile are to be 

plotted. (Default: false) 

LAbels 

A logical flag to indicate that room is to be made for color contour labels 

on the right side of the plot device. (Default: false) 


PLOT.2D 

L.Elect, L.Deple, L.Junct, L.Bound, L.Grid 

Integers to set line types for electrodes, depletion edges, junctions, region 

boundaries, and grids (i.e, mesh), respectively. (Defaults: 1) 

NO.Clear 

A logical flag to specify that the screen is not to be cleared before plotting. 


NO.Diag 

A logical flag to indicate not to plot the diagonals for a rectangle-based 

mesh. (Default: false) 

NO.Fill 

A logical flag to force the program to draw the device area plotted to scale. 

If this option is not specified, the plot will fill the screen and the triangles 

will appear distorted. (Default: false) 

NO.TIc 

A logical flag to indicate that tic marks are not to be included around the 

plotted area. (Default: false) 

NO.TOp 

A logical flag to indicate that tic marks are not to be put on the top of the 

plotted region. (Default: false) 

Outfile 

Character string for name of an output file in which the data points plotted 

are to be put. If specified, the graphics output will be directed to that file. 

For further discussion, see the Options card. (Default: from Options 

card) 


PLOT.2D 

Pause 

A logical flag causing the program to stop at the end of the plotting so that 

a hard copy may be made before continuing. Execution can be resumed by 

hitting a carriage return. (Default: false) 


Real number parameters to define a rectangular area in the device to be 

plotted. (Defaults: a rectangle encircling the entire device) 

EXAMPLES 

PLOT.2D GRID NO.FILL 

Plots the entire grid to scale with tic marks. 

PLOT.2D X.MIN=0 X.MAX=5 Y.MIN=0 Y.MAX=10 

+ JUNCT BOUND DEPL NO.TOP 

The device and region boundaries, junctions and depletion edges are 

plotted in the rectangular area bounded by 0 < x < 5 µ and 0 < y < 10 µ. 

The plot is allowed to fill the screen and tic marks are not included along 

the top of the plot. 


PRINT 

COMMAND 

PRINT 

The PRINT card prints specific quantities at grids within a defined area of 

the device. 

SYNTAX 

PRint 

location: 

{ X.MIn = X.MAx = 

Y.MIn = Y.MAx = } 

| 

{ IX.Low = IX.High = 

IY.Low = IY.High = } 

quantity: 

POints = Elements = 

Geometry = Solution = 

P.SOL1 = P.SOL2 = 

Current = P.CURR1 = 

P.CURR2 = Que = 

P.QUE1 = P.QUE2 = 

Material = 

flags: 

X.Compon = 

Y.Compon = 


PRINT 

PARAMETERS 

Current 

A logical flag to print currents (electron, hole, conduction, displacement, 

and total) at each grid for the present solution. (Default: false) 

Elements 

A logical flag to print information on triangular elements (sequence 

number, nodes, and material). (Default: false) 

Geometry 

A logical flag to print geometrical information (vertex coordinates) of 

triangles. (Default: false) 


Integers for bounding indices (valid only for a rectangular mesh) to define 

an area in which the points of interest lie. (Defaults: a rectangle encircling 

the entire device) 

Material 

A logical flag to print material information (permittivity, band-gap, etc.) 

including the value of the doping dependent mobility and lifetime (if 

model flags specified) at each grid. (Default: false) 

P.CURR1, P.CURR2 

Logical flags to print currents (electron, hole, conduction, displacement, 

and total) at each grid for previous first and second solutions, respectively. 



PRINT 

POints 

A logical flag to print grid information (coordinates, doping, etc.). 


P.QUE1, P.QUE2 

Logical flags to print space charge, recombination rate, and electric field 

for the previous first and second solutions, respectively. (Defaults: false) 

P.SOL1, P.SOL2 

Logical flags to print previous first and second solutions (ψ, n, p, and 

quasi-Fermi potentials), respectively. (Defaults: false) 

Que 

A logical flag to print space charge, recombination rate, and electric field 

for the present solution. (Default: false) 

Solution 

A logical flag to print the present solution (ψ, n, p, and quasi-Fermi 

potentials). (Default: false) 

X.Compon, Y.Compon 

Logical flags to specify how any of the various vector quantities (current 

and field) should be printed. The default is the magnitude of the vector. 

X.Compon specifies that the magnitude of the x-component of the vector 

be printed, while Y.Compon specifies the y-component. Only one of 

these (or neither) can be specified on a single card. (Defaults: false) 


Real number parameters for the physical coordinates, in units of µ, to 

define an area in which the points of interest lie. (Default: a rectangle 

encircling the entire device) 


PRINT 

EXAMPLES 

PRINT POINTS IX.LO=10 IX.HI=10 IY.LO=1 IY.HI=20 

Prints the physical coordinates, doping and region/electrode information 

for points along the 10th x grid line, from the 1st to the 20th y grid lines. 

PRINT SOLUTION X.MIN=0 X.MAX=1 Y.MIN=0 Y.MAX=2 

Solution information is printed for 0 < x < 1 µm and 0 < y < 2 µm. 


REGION 

COMMAND 

REGION 

The REGION card assigns material type and its composition, i.e., mole 

fraction profile for a compound semiconductor, to a rectangular region 

bounded by high and low node numbers in x- and y-directions. Every 

triangular element must be given a certain type of material. If there is an 

overlap among region assignments, the latter one takes precedence. 

Currently, there are four types of compound semiconductors available in 

the code and they are Ge x Si 1-x , Al x Ga 1-x As, Al x In 1-x As, and Ga x In 1- 

x As y P 1-y . The composition profile can be either constant or linear. 

SYNTAX 

REGIon 

number: 

NUmber = 

position: 

IX.Low = 

IY.Low = 

material: 

IX.High = 

IY.High = 

SILicon = | GAAs = | 

SIGe or GEsi = | ALGaas = | 

ALInas = | GAInasp = | 

SEmiconductor = | Oxide or SIO2 = | 

NItride or SI3n4 = | SApphire = | 

INsulator = 


REGION 

mole spec: 

XMole = YMole = 

YLinear = XInitial = 

{ XEnd = | XSlope = } 

YInitial = 

{ YEnd = | YSlope = } 

PARAMETERS 

ALGaas 

A logical flag indicating an Al x Ga 1-x As region. (Default: false) 

ALInas 

A logical flag indicating an Al x In 1-x As. (Default: false) 

GAAs 

A logical flag to indicate a gallium arsenide (GaAs) region. 


GAInasp 

A logical flag indicating a Ga x In 1-x As y P 1-y region. (Default: false) 

INsulator 

A logical flag to indicate a general insulator region. (Default: false) 


These parameters are the indices of a box in the rectangular mesh. 

(Default: the entire device) 


REGION 

NItride or SI3n4 

A logical flag to indicate a nitride (Si 3 N 4 ) insulator region. (Default: false) 

NUmber 

This parameter selects the rectangular region in question. Currently in the 

code the maximum number of regions is set to 1,000, but can be changed 

under the user's request. 

Oxide or SIO2 

A logical flag to indicate a silicon dioxide (SiO 2 ) region. (Default: false) 

SApphire 

A logical flag to indicate a sapphire (Al 2 O 3 ) region. (Default: false) 

SEmiconductor 

A logical flag to indicate a general semiconductor region. Forty material 

parameters can be defined by the user through MATERIAL card. (Default: 

false) 

SIGe or GEsi 

A logical flag indicating a Ge x Si 1-x region. (Default: false) 

SILicon 

A logical flag to indicate a silicon (Si) region. (Default: true) 

STrained 

A logical flag to indicate that the material is a strained layer. Currently in 

the code, it is only applied to Ga x In 1-x As y P 1-y and only the bandgap and 

the effective mass for holes (both light and heavy ones) are affected by this 

flag (for details see Section 4.4.3). (Default: false) 


REGION 

XInitial, XEnd, XSlope (YInitial, YEnd, YSlope) 

These real number parameters are used to specify the linear profile of mole 

fraction (x or y) in the region. Two combinations of parameters can be 

used to uniquely specify the profile. When XInitial and XEnd are used, 

the position-dependent mole fraction is computed as 

XEnd – XIinital 

mole( d) = XIinital + ---------------------------------------- ⋅ ( d – d (M.4) 

d high – d low ) 

low 

where d is either x or y depending upon the logical flag YLinear (see 

YLinear) and are coordinates corresponding to XInitial and 

d low 

d high 

XEnd, respectively. Another possible combination is for XInitial to be 

used with XSlope, the mole fraction is then computed as 

mole( d) = XIinital + XSlope ⋅ ( d – d low ) 

The same rules apply to y mole fraction. 

(M.5) 

XMole, YMole 

These real number parameters are used to specify the mole fraction for 

compound semiconductors, be binary (Ge x Si 1-x ), ternary (Al x Ga 1-x As and 

Al x In 1-x As), or quaternary (Ga x In 1-x As y P 1-y ). If the composition profile is 

flat (constant) in the region, the mole fraction is specified using XMole for 

x in binary/ternary and XMole and YMole for x and y, respectively, in 

quaternary. 

YLinear 

A logical flag to indicate that the linear composition profile changes along 

the y-direction instead of x-direction. (Default: false) 


REGION 

EXAMPLES 

REGION NUM=1 IX.LO=1 IX.HI=25 IY.LO=4 IY.HI=20 

+ SIL 

Defines a silicon region extending from nodes 1 to 25 in the x direction 

and nodes 4 to 20 in the y direction. 

Note that region cards are cumulative in effect: 


+ OXIDE 


+ OXIDE 

defines one region comprised of two separate strips. 

REGION NUM=1 IX.L=1 IX.H=100 IY.L=1 IY.H=3 

+ INSUL 


+ GAINASP XMOL=0.47 YMOL=1.0 







Defines an oxide layer partially overwritten by the source and drain 

regions consisting of Ga 0.47 In 0.53 As (y is set to 1.0 such that quaternary 

GaInAsP becomes ternary GaInAs). 


+ ALGAAS XINI=0.27 XEND=0.0 


REGION 


+ ALGAAS XMOLE=0.0 

This example shows the specification of linear grade of AlAs composition 

in Al x Ga 1-x As ternary along the y direction in region 2. 


REGRID 

COMMAND 

REGRID 

The REGRID card allows refinement of a crude mesh. Any triangle 

across which the chosen variable changes by more than a specified 

tolerance, or in which the chosen variable exceeds a given value, is 

refined. The default regrid is to refine all regions for potential and electric 

field. 

SYNTAX 

REGRid 

+ 

location: 

{ X.MIn = X.MAx = 

Y.MIn = Y.MAx = } | 

Region = | Ignore = 


Potential = | EL.field = | 

QFN = | QFP = | 

DOPIng = | ELEctrons = | 

Holes = | NET.CHarge = | 

NET.CArr = | Min.carr = 

control: 

STep or RAtio = CHange = 

ABsolute = LOGarithm = 

LOCaldop = MAx.level = 

SMooth.key =< logical> COs.angle= 


REGRID 

files: 

Outfile = 

AScii = 

DOPFile= 

PARAMETERS 

ABsolute 

A logical flag to specify that the absolute value of the quantity is to be 

used. (Default: false) 

AScii 

A logical flag to indicate that all mesh files and triangle trees (not 

including DOPFile) for this card should be done in ASCII rather than 

binary (a default). (Default: false) 

CHange 

A logical flag to determine whether to use the magnitude (false) or the 

difference (true) of a variable in a triangle as the criterion of refinement. 

(Default: true) 

COs.angle 

A real number for the cosine of the angle, which defines the “obtuse 

criterion'' to limit the creation of obtuse angles in the mesh. If regrid would 

create a triangle with an angle whose cosine ( cos ) is less than - 

COs.angle, nodes are added so that this does not occur. The test can be 

turned off locally by using the Ignore flag in this card. It can be turned off 

everywhere by using a value of COs.angle greater than 1.0. The default 

is to turn it off everywhere. (Default: 2.0) 


REGRID 

DOPFile 

Character string for the name of the binary mesh file, which contains the 

doping for the device (see DOPING card). If set to a non-null string, 

interpolation of doping values at any newly created grid points to re-dope 

the structure based on the initial doping specification (a default action) 

will not occur. (Default: null) 

DOPIng 

A logical flag to indicate regriding based on doping concentration (in units 

of cm -3 ). (Default: false) 

ELEctrons 

A logical flag to indicate regriding based on electron concentration (in 

units of cm -3 ). (Default: false) 

EL.field 

A logical flag to indicate regriding based on electric filed (in units of V/ 

cm). (Default: false) 

Holes 

A logical flag to indicate regriding based on hole concentration (in units of 

cm -3 ). (Default: false) 

Ignore 

An integer number for region(s). In these regions, regriding will not 

happen (i.e., ignored), nor will be smoothed after regriding. This flag is 

similar to REGion in function, but opposite in effect. (Default: 0, i.e., 

none ignored) 


REGRID 

LOCaldop 

A logical flag related to the minority carrier regrids. If set, when the 

minority carrier concentration exceeds the local doping, the grid will be 

refined. (Default: false) 

LOGarithm 

A logical flag to use logarithmic instead of the actual value of the quantity 

concerned. If set, parameter STep (RAtio) is interpreted in the logarithm. 

(Default: false.) 

MAx.level 

An integer for the maximum level of any triangle relative to the original 

mesh. It defaults to one more than the maximum level of the grid, but can 

be set to a smaller value to limit refinement. Values less than or equal to 

zero are interpreted relative to the current maximum level. (Default: 

dynamic) 

MIn.carr 

A logical flag to indicate regriding based on minority carrier concentration 

(in units of cm -3 ). (Default: false) 

NET.CHarge 

A logical flag to indicate regriding based on the net charge density (in 


NET.CArr 

A logical flag to indicate regriding based on net carrier concentration (in 


Outfile 

Character string for the binary output mesh file, which is necessary if the 

mesh is to be used for subsequent runs. A history of the triangle tree is 


REGRID 

always generated to assist further regriding steps and its name is the one 

specified by Outfile and concatenated by the letters “tt” to the end. In the 

case that this file is used as an input mesh file for a PISCES run including 

a regrid action, the program will look for a file with the same name as the 

input mesh file plus “tt” at the end. (Default: null) 

Potential 

A logical flag to indicate regriding based on electrostatics potential which 

usually refers to the intrinsic Fermi level (in units of V). (Default: false) 

QFN, QFP 

Logical flags to indicate regriding based on electron and hole quasi-Fermi 

levels, (in units of cm -3 ), respectively. (Defaults: false) 

Region 

An integer for region(s) in which mesh is to be refined according to the 

user criterion. Note that other regions might be refined as well as a side 

effect to maintain well-shaped triangles. (Default: all regions) 

SMooth.key 

An integer parameter which has the same meaning as SMooth.key in 

MEsh card. See MEsh card for details. (Default: 0) 

STep (RAtio) 

Real number parameter as the numerical criterion for refining a triangle. It 

is interpreted in logarithm if flag LOGarithm is set. (No default) 


Real number parameters for the bounds of the region for mesh refinement; 

Only those triangles which have nodes falling inside the region are 

considered for refinement. (Defaults: a rectangle encircling the entire 

device). 


REGRID 

EXAMPLES 

REGRID LOG DOPING STEP=6 OUTF=grid1 DOPF=dopxx1 


Starting with an initial grid, we refine twice, requesting that all triangles 

with large doping steps be refined. 


+ MAX.LEVEL=2 

A similar effect is obtained with just one REGRID statement. In both 

cases two levels of refinement are done. The first choice is preferable 

however, because new doping information is introduced at each level of 

refinement. This gives a better criterion for refinement, and fewer 

triangles. 

SOLVE INIT OUT=grid2.si 

REGRID POTENTIAL STEP=0.2 OUTF=grid3 

This time we perform an initial solution and refine triangles which exhibit 

large potential steps. 


SOLVE 

COMMAND 

SOLVE 

The SOLVE card instructs PISCES to perform a solution for one or more 

specified bias points. 

SYNTAX 

SOLve 

+ 

initial guess: 

{ INitial = | PREvious = | 

EXtrapolate = | PROject = | 

LOCal = } 

dc bias: 

V1 = I1 = T1 = 

V2 = I2 = T2 = 

. . . 

V9 = I9 = T9 = 

V0 = I0 = T0 = 

ELectrode = VSTep = 

IStep = NSteps = 

N.bias = P.bias = 

transient: 

Dt or TSTEp = TSTOp or TFinal = 

Ramptime = ENdramp = 


SOLVE 

ac: 

{{ AC.analysis = FRequency = 

SOr = Qmr = 

FStep = MUlt.freq = 

NFstep = VSS = 

S.omega = MAx.inner = 

TOlerance = 

} | LOWfreq.ac = 

} TErminal = 

files: 

Outfile = 

Currents = 

AScii = 

BAnd = 

PARAMETERS 

AC.analysis 

A logical flag to indicate that AC sinusoidal small-signal analysis be 

performed after the DC condition is solved for. Note that the full Newton 

method (2 carriers) must be used for this analysis. Use of flag G.Debug 

in the Options card will provide some detailed information on the AC 

solution procedure. (Default: false) 

AScii 

A logical flag to indicate that the solution file saved in Outfile will be 

ASCII as opposed to binary (a default). (Default: false) 


SOLVE 

BAnd 

A logical flag to include the band profile (vacuum level, conduction and 

valence band edges) in the output solution file in addition to potential, 

carrier concentrations, etc. (Default: false) 

Currents 

A logical flag to indicate that the electron, hole, and displacement 

currents, and the electric field, will be computed and stored with the 

solution. (Default: false) 

Dt or TSTEp 

Real number for the time-step to be taken during time transient analysis. 

For automatic time-step runs (flag TAuto in MEthod card), it is used to 

select the first time step only. (Default: 0.0) 

ELectrode 

An integer for the number of the electrode being stepped. If more than one 

electrode is to be stepped, ELectrode should then be an n-digit integer, 

where each of the n-digits is a separate electrode number. Note that if there 

are 10 electrodes, don't put electrode 0 first in the sequence!). (Default: 0) 

EXtrapolate 

A logical flag to indicate that the initial guess for the solution at the 

present bias is to be obtained by linear extrapolation of the previous two 

solutions which are either just obtained in the current PISCES run or 

loaded in using parameters IN1file and IN2file in LOad card. 


FRequency 

Real number parameter for the frequency, in units of Hz, at which AC 

analysis is to be performed. (No default) 


SOLVE 

FStep, MUlt.freq, NFstep 

The AC analysis can be repeated at a number of different frequencies 

(without resolving the DC condition) by selecting a real number parameter 

FStep. FStep is a frequency increment which is added to the previous 

frequency by default, or it may be multiplied to by setting logical flag 

MUlt.freq. The number of increments is given by integer parameter 

NFsteps. (Defaults: FStep, 0.0; MUlt.freq, false; NFsteps, 0) 

INitial 

A logical flag to indicate the solution at the thermal equilibrium (i.e., zero 

bias) is to be sought. Note that the first bias point in any PISCES run must 

be set with this flag unless there is a solution loaded using LOad card. 


IStep 

Real number parameter for the current increment to be added to one or 

more electrodes, as specified by the integer assigned using parameter 

ELectrode in this card. (Default: 0.0) 

I1, I2, ... , I9, I0 

Real number parameters for the terminal currents, in units of A µ −1 , 

applied to contacts 1, 2, ... , 9, 0. (Default: currents from the previous 

solution) 

LOCal 

A logical flag to use the carrier quasi-Fermi levels in the previous solution 

(INFile in LOAd card) as the initial guess. (Default: false) 

LOWfreq.ac 

A logical flag to use zero-frequency for AC analysis (see Section 5.1.4 for 

details). (Default: false) 


SOLVE 

MAx.inner 

Integer parameter for the maximum number of SOR iterations. 

(Default: 25) 

N.bias, P.bias 

Real number parameters to set the levels for electron and hole quasi-Fermi 

potentials, respectively. These parameters only apply to those carriers 

which are not being solved for in the PISCES run (e.g. holes when only 

electrons are specified to solve in Solve card). If N.bias or P.bias is not 

specified, then program will either choose local quasi-Fermi potentials 

based on bias and doping (see Chapter 2 of [3]) or if Fix.qf is set on the 

MEthod card, set the quasi-Fermi levels where applicable to values which 

produce the least amount of free carriers (maximum bias for electrons and 

minimum bias for holes). 

NSteps 

The number of bias increments (steps) to be taken; i.e., if VStep (IStep) 

is specified, the specified electrode is incrementted NSteps times. 


Outfile 

Character string for the name of the binary output file to save the solution 

at this bias point. If an electrode is stepped so that more than one solution 

is generated by this card, the last non-blank character of the supplied file 

name will have its ASCII code incrementted by one for each bias point in 

succession, resulting in a unique file for each bias point. (Default: null) 

PREvious 

A logical flag to specify that the solution at the previous bias point, either 

loaded in using LOad card or just solved, be used as the initial guess for 

the solution at the present bias point. (Default: true) 


SOLVE 

PROject 

A logical flag to indicate Newton Projection method (NPM) is to be used 

in obtaining the initial guess to the solution at the present bias based on the 

previous solution. For details of NPM, see Section 5.4. (Default: false) 

Qmr 

A logical flag to use QMR (Quasi-Minimal Residual) method for AC 

analysis (see Section 5.1.3 for details) (Default: true) 

Ramptime, ENdramp 

Real number parameters to specify the time duration of a bias ramp and 

the ending instant of the ramp, respectively, for transient analysis, in units 

of seconds. Note that bias ramp must be linear. Specifically, is the ramp 

begins at t = t 0 , then it ends either at t = t 0 + Ramptime or at t = 

ENdramp, depending on which parameter is used. (Defaults: 0.0) 

S.omega 

A real number parameter for the relaxation factor used in SOR method ( ν 

in Eqs. (5.13)-(5.14)). Note that it is not a frequency. (Default: 1.0) 

SOr 

A logical flag to use SOR method for AC analysis (refer to Section 5.1.1. 

and [36] for details) (Default: false) 

TErminal 

An integer parameter for the sequence number of contact(s) to which the 

AC bias (i.e., stimulus) is to be applied. More than one contact number 

may be specified (via concatenation), but each will be solved separately. 

Each contact that is specified yields a column of the admittance matrix. 

(Default: all contacts) 


SOLVE 

TOlerance 

Real number parameter used as the criterion for the iteration to terminate 

in AC analysis, unitless. (Default: 1×10 

) 

TSTOp (TFinal) 

Real number parameter to specify the end of the time interval to be 

simulated, in units of seconds. Thus the simulation begins at t = t 0 , it will 

end at t = TSTOp (TFinal). Alternatively, NSteps can be used to signal 

the end of the interval; That is, the final time would be t = t 0 + NSteps x 

TSTEp. (Default: 0.0) 

T1, T2, ... , T9, T0 

Real number parameters for the lattice temperatures at terminals (either 

thermal or electrical) if thermal Dirichlet boundary conditions are applied 

to the corresponding contacts. (Defaults: from previous solution) 

VSS 

Real number parameter for the magnitude of the applied small-signal bias 

(stimulus) (V i in Eq. (2.19) of [4]). (Default: 0.1 x kT/q where T is the 

environment temperature) 

VSTep 

Real number parameter for the voltage increment to be added to one or 

more electrodes, as specified by the integer assigned to parameter 

Electrode in Solve card. (Default: 0.0) 

V1, V2, ... , V9, V0 

Real number parameters for the bias voltages (for non-current boundaries 

only) applied at contacts 1, 2, ... , 9, 0. (Default: the potentials from the 

previous solution) 

–5 


SOLVE 

EXAMPLES 

SOLVE INIT OUTF=OUT0 

Performs an initial bias point, saving the solution to the data file OUT0. 

SOLVE PREV V1=0 V2=.5 V3=-.5 OUTF=OUT1 

SOLVE V1=1 V2=.5 V3=0 VSTEP=1 NSTEPS=4 

+ ELECT=1 OUTF=OUTA 

In this example, bias stepping is illustrated. The two SOLVE cards 

produce the following bias conditions: 

Bias point # V1 V2 V3 

1 0.0 0.5 0.5 

2 1.0 0.5 0.0 

3 2.0 0.5 0.0 

4 3.0 0.5 0.0 

5 4.0 0.5 0.0 

6 5.0 0.5 0.0 

The solutions for these bias points will be saved to the files OUT1, OUTA, 

OUTB, OUTC, OUTD and OUTE. Note that the initial guess for the first 

bias point is obtained directly from the preceding solution because the 

PREvious option was specified. The initial guesses for bias points 2 and 

3 will also be obtained as if PREvious had been specified since two 

electrodes (numbers 1 and 3) had their biases changed on bias point 2. 

However, for bias points 4, 5 and 6, PISCES-II will use a projection to 

obtain an initial guess since starting with bias point 4, both of its preceding 

solutions (bias points 2 and 3) only had the same electrode bias (number 1) 

altered. 


SOLVE 

SOLVE V1=0 V2=0 V3=1 VSTEP=.5 NSTEPS=2 ELECT=23 

SOLVE V2=2 V3=3 

Here is a case where two electrodes are stepped (2 and 3). The bias points 

solved for will be (0,0,1), (0,.5,1.5), (0,1,2) and (0,2,3). PISCES-II will 

use the PROject option to predict an initial guess for the third and fourth 

bias points since the bias voltages on both electrodes 2 and 3 have been 

altered by the same amount between each point. 

SOLVE V1=0 V2=0 V3=1 

SOLVE VSTEP=.5 NSTEPS=2 ELECT=23 

SOLVE VSTEP=1 NSTEPS=1 ELECT=23 

This repeats the previous example as a three-card sequence. If no new 

voltages are specified and a VStep is included, the first bias point solved 

for is the preceding one incrementted appropriately by VStep. 

METHOD 2ND TAUTO AUTONR 

SOLVE V1=1 V2=0 

SOLVE V1=2 TSTART=1E-12 TSTOP=25E-9 

+ RAMPTIME=10E-9 OUTF=UP1 

SOLVE V1=-1 TSTOP=100E-9 RAMPTIME=20E-9 

+ OUTF=DOWN1 

SOLVE V1=-1 V2=0 

This sequence is an example of a time-dependent solution. The 

METHOD card specifies the second-order discretization and automatic 

time-step selection option, along with Newton-Richardson. The first 

SOLVE card then computes the solution for a device with 1 volt on V1 

and 0 on V2 in steady-state. The second SOLVE card specifies that V1 is 

to be ramped to 2 volts over a period of 10ns and is left on until 25ns. Each 

solution is written to a file; the name of the file is incrementted in a 

manner similar to that described above for a dc simulation (UP1, UP2, 

etc.). Note that an initial time step had to be specified on this card. The 

third SOLVE card ramps V1 down from 2 volts to -1 volts in 20 ns (end of 


SOLVE 

ramp is at t = 45ns). The device is then solved at this bias for another 55ns 

(out to 100ns). Note that again each solution is saved in a separate file 

(DOWN1, DOWN2, etc.) and that no initial time-step was required since 

one had been estimated from the last transient solution for the previous 

SOLVE card. Finally, the fourth SOLVE card performs the steady-state 

solution at V1 = -1 and V2 = 0.0 

SOLVE V1=0 V2=0 V3=0 VSTEP=0.5 NSTEPS=4 

+ ELECT=1 AC FREQ=1E6 FSTEP=10 MULT.F 

+ NFSTEP=5 VSS=0.01 

Here an AC example is presented. Assume the device to be simulated has 

3 electrodes. Starting from solved DC conditions at V1 = 0, 0.5, 1.0, 1.5 

and 2.0 volts, 10 mV AC signals of frequency 1 MHz, 10 MHz, 100 MHz, 

1 GHz, 10 GHz and 100GHz are applied to each electrode in the device. 

Note that the number of AC solutions to be performed is 5 X 6 X 3 = 90. 

SOLVE V1=0 V2=0 V3=0 VSTEP=0.5 NSTEPS=4 

+ ELECT=1 lowf 

Same as the above example but use zero-frequency analysis to extract 

quasi-static y-parameters. 


SPREAD 

COMMAND 

SPREAD 

The SPREAD card provides a way to distort rectangular grids in the 

vertical direction to follow surface and junction contours. SPREAD is 

very useful in reducing the amount of grid for some specific problems, 

most notably MOSFETs. The SPREAD card is somewhat complicated; it 

is suggested to follow the supplied examples very carefully (particularly 

the MOSFET example in Chapter 5 in [3]). 

SYNTAX 

SPread 

direction: 

{ LEft = | Right = } 

region: 

Width = 

Upper = 

LOwer = 

specifics: 

{ Y.Lower = | Thickness = } 

Vol.ratio = Encroach = 

GRAding = 

GR1 = GR2 = 

Middle = Y.Middle= 


SPREAD 

PARAMETERS 

Encroach 

A real number factor which defines the abruptness of the transition 

between a distorted and non-distorted mesh. The transition region 

becomes more abrupt with smaller Encroach factors (the minimum is 

0.1). An important note: depending on the characteristics of the 

undistorted mesh, very bad triangles (long, thin, and obtuse) may result if 

Encroach is set too low. (Default: 1.0) 

GRAding 

A real number parameter to specify a grid ratio (identical to the Ratio 

parameter on the X.Mesh and Y.Mesh cards) to produce a non-uniform 

grid in the distorted region. (Default: 1.0) 

GR1, GR2, Middle, Y.Middle 

Real number parameters used as an alternative to a single GRAding 

parameter. GR1 and GR2 can be specified along with the y grid line 

Middle and location Y.Middle so that GR1 is used as the grading in the 

spread region from Upper to Middle and GR2 is the grading from 

Middle to LOwer. (Defaults: GR1, 1.0; GR2, 1.0; and no defaults for 

Middle and Y.Middle) 

LEft, Right 

Logical flags to specify that the left and right sides of the grid, 

respectively, will be distorted. (Defaults: false) 

Upper, LOwer 

Integer parameters to specify the upper and lower y-grid lines, 

respectively, between which the distortion will take place. (No default) 


SPREAD 

Vol.ratio 

Real number parameter as the ratio of the downward displacement of the 

lower grid line to the net increase in thickness. It is ignored if Y.Lower is 

specified. (Default: 0.44 which is derived from oxide/silicon growth/ 

consumption ratio during oxidation such that the Si/SiO 2 interface can 

move correctly) 

Width 

A real number parameter to specify the width from the left or right edge 

(depending on the LEft and Right parameters) of the distorted area. The 

actual x-coordinate specified by Width (min[x] + Width for LEft and 

max[x] - Width for Right) will lie in the middle of the transition region 

between the distorted and undistorted grid regions, in units of 

default) 

µ . (No 

Y.Lower and Thickness 

Real number parameters to define the distorted grid region, in units of µ . 

Only one of them should be supplied. Y.Lower is the physical location in 

the distorted region at which the line specified by LOwer will be moved. 

The line specified by Upper is not moved. Thickness is the thickness of 

the distorted region and it will usually move the positions of both the 

Upper and LOwer grid lines unless Vol.ratio is set to 0 or 1. (No 

default) 

EXAMPLES 

$ *** Mesh definition *** 

MESH NX=30 NY=20 RECT 

X.M N=1 L=0 

X.M N=30 L=2 

Y.M N=1 L=-.04 


SPREAD 

Y.M N=5 L=0 

Y.M N=20 L=1 R=1.4 

$ *** Thin oxide *** 

REGION X.L=1 X.H=30 Y.L=1 Y.H=5 

$ *** Silicon substrate *** 

REGION X.L=1 X.H=30 Y.L=5 Y.H=20 

$ *** Spread *** 

SPREAD LEFT WIDTH=0.5 UP=1 LO=5 THICK=0.1 

ENC=1.3 

This spreads what was previously a uniform 400Å of oxide to 1000Å on 

the left side of the device. This will result in a net increase in thickness of 

600Å of oxide. Because the default Vol.ratio is used, 0.44 X (600) = 

264Å of the net increase will lie below the original 400Å and 0.56 X (600) 

= 336Å of the net increase will lie above the original 400Å. The width of 

the spread region is 0.5 µm and the oxide taper is quite gradual because of 

the high encroachment factor. The grid is left uniform in the spread region. 

DOPING UNIFORM N.TYPE CONC=1E15 

DOPING GAUSS P.TYPE X.LEFT=1.5 X.RIGHT=2 

+ PEAK=0 CONC=1e19 RATIO=.75 JUNC=0.3 

SPREAD RIGHT WIDTH=0.7 UP=5 LO=10 Y.LO=0.3 

+ ENC=1.2 GRAD=0.7 

The right side of the grid is distorted in order to follow a junction contour. 

Assume that the initial grid is defined as above. Y.Lower is used so that 

there is no increase in the size of the device, just grid redistribution. With 

Y.Lower set to the junction, the Encroach parameter should be chosen 

such that the lower grid line (LOwer=10) follows the junction as closely 

as possible. Note that the grid is graded so that the grid lines are spaced 

closer together as they approach the junction. Because the point specified 

by Width on the SPREAD card lies in the middle of the transition region, 

it should be chosen to be slightly larger than the width of the doping “box'' 

(Width < X.Left - X.Right = 0.5 µm). 


SYMBOLIC 

COMMAND 

SYMBOLIC 

The SYMBOLIC card performs a symbolic factorization in preparation 

for the LU decompositions in the solution phase of PISCES. Because 

each of the available numerical solution techniques used by PISCES may 

result in entirely different linear systems, the method used and the number 

of carriers to be simulated must be specified at this time. The symbolic 

factorization may be optionally read from or written to a file; if an input 

file is specified, the symbolic factorization information in that file must be 

consistent with the method specified on the present card. 

SYNTAX 

SYmbolic 

+ 

solution method: 

{ Newton = | Gummel = } 

device equation: 

Carriers = 

{ Electrons = | Holes = } 

ENGY.Elect = | ENGY.Hole = 

ENGY.Lat = 

options: 

Min.degree = Strip = 

Infile = Outfile = 

Print = 


SYMBOLIC 

PARAMETERS 

Carriers 

An integer parameter to specify the number of types of carriers to be 

simulated. 0 for solving the Poisson’s equation only, 1 for solving either 

electrons or holes depending on flags ELectrons and Holes, and 2 for 

solving both electrons and holes. (Default: 1) 

ELectrons, Holes 

Logical flags to indicate which type of carriers is to be solved if Carriers 

is set to 1. (Defaults: false) 

ENGY.Elect, ENGY.Hole 

Logical flags to indicate if electron or hole or both carrier energy balance 

equation(s) is to be solved in the simulation. (Defaults: false) 

ENGY.Lat 

A logical flag to indicate that the lattice thermal diffusion equation is to be 

solved during the simulation. (Defaults: false) 

Infile, Outfile 

Character strings (up to 20 characters long) to specify the input and output 

(binary) file names, respectively, for the symbolic factorization. Note that 

these binary files can be quite large, so it is advised not to use this feature. 

(In some computing environments it is also faster to compute the symbolic 

information for each run than to read it from the file). (No default, strings 

set to null) 


SYMBOLIC 

Min.degree 

A logical flag to specify the use of a minimum degree ordering of the 

pivots for decomposition in order to reduce the size of the generated L and 

U matrices, hence to reduce the amount of CPU time spent in solving 

linear systems. This parameter is definitely recommended. (Default: true) 

Newton, Gummel 

Logical flags to specify the Newton simultaneous or Gummel sequential 

method in solving the Poisson’s, electron and hole continuity equations. In 

the case of solving the Poisson’s equation only (Carriers = 0), Gummel 

method is the default one. When one of or both carrier energy balance 

equations is to be solved, Newton method must be used for the current 

implementation. (Defaults: false) 

Print 

A logical flag to indicate that information about the memory allocated for 

the run is to be printed to the standard output file. (Default: false) 

Strip 

A logical flag to specify redundancy (zero couplings) be removed from the 

symbolic map, and is naturally on. (Default: true) 

EXAMPLES 

SYMBOLIC GUMMEL CARR=1 HOLES OUTF=SYMB.OUT 

Specifies a symbolic factorization for a simulation with only holes and 

using the Gummel method (the symbolic factorization is saved in a file 

called SYMB.OUT). 


SYMBOLIC 

SYMBOLIC NEWTON CARR=2 INF=SYMB.IN PRINT 

A previously generated symbolic factorization is read in from a file called 

SYMB.IN. The method used is the full Newton method, and both carriers 

are included in the simulation. Additionally, the sizes and dimensions of 

all arrays associated with the sparse matrix solution are printed. 

SYMBOLIC NEWTON CARR=2 engy.ele 

Solve electron energy balance equation together with Poisson’s and two 

carrier continuity equations for electron temperature and ψ , n, and p. 


TITLE 

COMMAND 

TITLE 

The TITLE card specifies a title (up to 60 characters) to be used in 

PISCES standard output. 

SYNTAX 

Title 

 

PARAMETERS 

None. 

EXAMPLES 

TITLE *** CMOS p-channel device *** 


VECTOR 

COMMAND 

VECTOR 

The VECTOR card plots vector quantities over an area of the device 

defined by the previous PLOT.2D card. 

SYNTAX 

Vector 


{ J.Conduc = | J.Electr = | 


J.Total = | E.field = } 

control: 

LOgarithm = MInimum = 

MAximum = Scale = 

Clipfact = LIne.type = 

PARAMETERS 

Clipfact 

A threshold below which vectors are not plotted. (Default: 0.1) 

E.field 

Plot the electric field. (Default: false) 


VECTOR 

J.Conduc, J.Displa, J.Electr, J.Hole, J.Total 

Logical flags for plotting the conduction, displacement, electron, hole, and 

total current densities, respectively. (Defaults: false) 

LIne.type 

An integer parameter for the vector line type for plotting. (Default: 1, a 

solid line) 

LOgarithm 

A logical flag to specify use of logarithmic value of the magnitude. By 

default, all vectors in a linear plot are scaled by the maximum magnitude 

of the quantity of interest over the grid, while if LOgarithm is set, the 

default scaling uses the minimum (non-zero) magnitude. (Default: false) 

MAximum, MInimum 

Real number parameters for the minimum and maximum values of the 

quantities to be plotted. These values will be printed during the execution 

of a plot. With these parameters is possible to plot two bias conditions or 

two devices with the same scaling. (Defaults: 0.0) 

Scale 

A real number parameter used as the scale factor by which all magnitudes 

are multiplied. (Default: 1.0) 

EXAMPLES 

PLOT.2D BOUN NO.FILL 

VECTOR J.ELEC LINE=2 

VECTOR J.HOLE LINE=3 

Plot electron and hole currents over a device. 


X.MESH, Y.MESH 

COMMAND 


The X.MESH and Y.MESH cards specify the location of lines of nodes 

in a rectangular mesh. 

SYNTAX 

X.mesh or Y.mesh 

node: 

location: 

Node = 

ratio: 

Location = 

Ratio = 

PARAMETERS 

Location 

Real number parameter to specify where to locate the line, in units of µ . 

(No default) 

Node 

An integer parameter for the numbering of the line in the mesh. Lines 

should be assigned consecutively, beginning with the first and ending with 

the last. (No default) 



Ratio 

Real number parameter as the ratio used for the interpolation of lines 

between the given lines, unitless. The spacing grows/shrinks by ratio in 

each subinterval, and the ratio should usually lie between 0.667 and 1.5. 


EXAMPLES 

Y.MESH N=1 LOC=0.0 

Y.MESH N=20 LOC=0.85 RATIO=0.75 

Y.MESH N=40 LOC=2 RATIO=1.333 

Space grid lines closely around a junction in a 1-d diode with the junction 

at 0.85 microns. 


PART II 

Curve Tracer 

Stephen G. Beebe, Zhiping Yu, Ronald J. G. Goossens, 

and Robert W. Dutton


This project was supported by Semiconductor Research Corporation Contract Numbers, SRC 94-SJ- 

116 and SRC 93-MC-106. We would also like to acknowledge the mentorship of Dr. Ben Tseng of 

AMD as well as AMD’s support of both a summer internship and ongoing access to their facilities and 

device technology during the period of this study. 

Curve Tracer 235

236 Curve Tracer

SECTION 7 

Introduction 

In Technology CAD, the use of software to simulate the testing of semiconductor devices is known as 

the Virtual Instrumentation. A virtual instrument should be able to automatically generate simulation 

data, e.g., I-V curve along a bias sweep, given only the simple specifications a user would input to a 

real programmable instrument testing an IC device. Numerical device simulators such as PISCES 

provide a means of creating virtual devices and simulating electrical tests on the devices. However, 

these simulators cannot trace through I-V curves with sharp turns unless the user carefully controls the 

bias conditions near these turns -- a tedious and time-consuming process. This deficiency prompted 

the creation of Tracer. 

Tracer is a C program which automatically guides PISCES and other semiconductor device 

simulators through complex I-V traces and is ideally suited for device-failure phenomena such as 

latchup, BV CEO , and electrostatic-discharge (ESD) protection. Given a PISCES input deck and a 

specification file with a PISCES-like syntax, a simulation can be run over any current or voltage range 

without the user’s intervention. Tracer is limited to DC, one-dimensional traces, i.e., only one 

electrode can be swept per run. It sweeps the electrode by dynamically setting the most stable bias 

condition at each solution point. Additionally, Tracer has the ability to maintain zero-current bias 

conditions at one or two electrodes during the trace, even at low device-current levels where such bias 

conditions are unstable using traditional device simulation. The theory implemented in the Tracer 

program can be found in [1]. 

Curve Tracer 237

SECTION 8 

Shell Command Line 

Usage: %tracer inputfile tracefile [outputfile] 

where 

• tracer is the program name, i.e. it is the shell command name 

• inputfile is the name of the PISCES input deck which defines the device structure to be 

simulated and specifies what physical models are to be used. Basically, it contains everything 

in a normal PISCES deck except the solve card specifications (SECTION 10). 

• tracefile is a file containing instructions on how to conduct the tracing as well as 

specifying bias conditions for all electrodes (SECTION 9). 

• outputfile is an optional specification of the name of the file where the simulation data is 

to be written (SECTION 11). If outputfile is not given, the name of the output file defaults 

to inputfile.out. 

238 Curve Tracer

SECTION 9 

Trace File 

The trace specification file, tracefile, is similar to a PISCES or SUPREM input deck. Each line 

begins with a word designating what type of statement (or “card”) it is. The four available cards are 

CONTROL, FIXED, OPTION, and SOLVE. Also, a line may start with a “$” for comments. Such 

lines are ignored during program execution. The cards may appear in any order. A card may be 

continued on following lines by placing a “+” at the beginning of each subsequent line. The “+” should 

be separated from the parameters on the line by at least one space. 

Each option in a card should have the following structure: “param = paramvalue”. Spaces 

separating the “=” sign are optional. The parameters for each card are described below. As with 

PISCES syntax, parameter names and values are not case-sensitive and may be abbreviated provided 

they remain unambiguous. Square brackets, [], enclosing a parameter indicate that it is optional (note 

that some of these parameters are optional only in the sense that they will default to a certain value if 

not specified in tracefile). A vertical line, |, represents a logical OR -- only one of a list of 

parameters separated by “|” signs can be specified. 

All electrodes in the device must have representation in the tracefile. Each electrode 

must appear as one, and only one, of the following: the CONTROL electrode, a FIXED electrode, or 

an open contact (OPENCONT1 or OPENCONT2) on the SOLVE card. 

Curve Tracer 239

Trace File 

9.1 CONTROL Card 

9.1.1 Description 

The CONTROL card is used to designate the electrode which will be swept through the trace as well 

as the boundaries of the trace. This electrode is referred to as the control electrode. To define the start 

of the simulation range, an initial voltage and an initial voltage step must be specified for the control 

electrode. The end of the trace is specified by either a maximum electrode voltage, a maximum 

electrode current, or the total number of simulated points to be found. 

9.1.2 Syntax 

NUM= CONTROL= [BEGIN=] [INITSTEP=] 

[ENDVAL= | STEPS=] 

9.1.3 Parameters 

• NUM is the sequence number of the electrode in the PISCES input deck designated as the 

control electrode, whose voltage or current is swept through the trace. Its integer value must be 

between 1 and 9, inclusive. (Default: none) 

• CONTROL is either VMAX, IMAX, or STEP. VMAX denotes that a maximum voltage on 

the control electrode, specified by ENDVAL, is used as the upper bound on the trace. IMAX 

denotes that ENDVAL specifies a maximum control-electrode current for the trace. STEP 

signifies that the trace will proceed for a certain number of simulation points, specified by the 

STEPS parameter. In most cases VMAX or IMAX will be used because it is not known how 

many simulation steps will be taken to reach a certain voltage or current. (Default: none) 

• BEGIN is the value of the voltage, in volts, at the starting point of the curve trace for the 

electrode designated by NUM (the control electrode). If an initial solution is performed by 

Tracer, BEGIN should be 0.0. If a previous solution is loaded into the input deck at the start 

of Tracer (see SOLVE card below), BEGIN should be equal to the voltage of the control 

electrode in this solution. (Default: 0.0V) 

• INITSTEP is the initial voltage increment, in volts, of the control electrode. Thus, at the 

second solution point the control electrode will have a voltage of BEGIN + INITSTEP. A 

recommended initial step size is 0.1V. The sign of INITSTEP determines the direction in 

240 Curve Tracer

Trace File 

which the curve tracing will initially be proceeded. If INITSTEP proves to be too large and 

PISCES cannot converge on the second solution point, Tracer will automatically reduce 

INITSTEP until convergence is attained, then proceed with the trace from this point. (Default: 

0.1V) 

• ENDVAL is used when CONTROL=VMAX or IMAX. Tracer stops tracing when the 

voltage (CONTROL=VMAX) or current (CONTROL=IMAX) of the specified electrode 

equals or exceeds the value specified by ENDVAL. Note that it is the absolute values of the 

voltage or current and of ENDVAL which are compared. (Default: 10.0V 

(CONTROL=VMAX), 10.0A/µm (CONTROL=IMAX)) 

• STEPS is used when CONTROL=STEP. It specifies the number of solution points Tracer 

should find. (Default: 10) 

9.1.4 Examples 

1. Electrode 3 is the control electrode. Tracer will initially proceed in the negative-voltage direction 

with an initial step of -0.1V. Tracer will proceed until the absolute value of the control current 

equals or exceeds 3A/µm. 

control num=3 begin=0.0 initstep=-0.1 control=IMAX end=-3.0 

2. Electrode 4 is the control electrode. Tracer will run until 65 solutions are found, starting at 

v4=0.0V with an initial v4 step of 0.5V. 

control num=4 begin=0.0 initstep=0.5 control=step steps=65 

9.2 FIXED Card 


A FIXED card is used to designate an electrode whose bias remains fixed throughout the simulation. 

There should always be at least one FIXED electrode and usually there are two or more. The two types 

of bias conditions available are voltage sources and current sources. The value of the bias is arbitrary, 

with one exception: a zero-current source (open contact) should be specified through the open-contact 

option on the SOLVE card and not on the FIXED card. If non-zero current sources are used for some 

Curve Tracer 241

Trace File 

electrodes in a simulation, in inputfile the user must create contact cards with the “current” option 

for each of these electrodes (see SECTION 10). 

9.2.2 Syntax 

NUM= [TYPE=] [VALUE=] [RECORD=] 


• NUM is the sequence number of an electrode in the PISCES deck. Its integer value must be 

between1 and 9, inclusive. (Default: none) 

• TYPE is either VOLTAGE or V for a voltage source or CURRENT or I for a current source. 

(Default: VOLTAGE) 

• VALUE is the fixed value of the current or voltage for the electrode specified by NUM. 

VALUE has units of either volts or amps/µm, depending on the specification of TYPE. Note 

that the specification of VALUE is optional since it is merely for reference and is not used by 

Tracer. (Default: 0.0) 

• RECORD is either YES or NO. For RECORD=YES, the simulated current is recorded in the 

output file for a fixed-voltage electrode, while the simulated voltage is recorded for a fixedcurrent 

electrode. (Default: NO) 


In every Tracer solution, electrode 1 has a voltage of 0.0V. The current in this node is recorded in 

outputfile at every solution point. 

fixed num=1 type=voltage value=0.0 record=yes 

9.3 OPTION Card 


An OPTION card is used to specify convergence criteria and solution-method options for any open 

electrodes, parameters which affect the smoothness and step-size control of the trace, which PISCES 

solution files are saved, and whether extra solution data is saved in outputfile. 

242 Curve Tracer

Trace File 

9.3.2 Syntax 

Simulations with one or two open contacts: 

[ABSMAX=] [RELMAX=] [DAMP=] [TRYCBC=] 

Smoothness and step-size control: 

[ANGLE1=] [ANGLE2= [ANGLE3=] [ITLIM=] 

[MINCUR=] [MINDL=] 

Control of output files: 

[FREQUENCY=] [TURNINGPOINTS=] [VERBOSE=] 


• ABSMAX is the maximum current allowed in an open contact and is only relevant when open 

contacts are used and voltage biases are applied to these contacts. Convergence is satisfied 

–19 

when either the ABSMAX or RELMAX condition is met. (Default: 1.0×10 A/ µ m) 

• RELMAX is the maximum ratio of open-contact current to control-electrode current and is 

only relevant when open contacts are used and voltage biases are applied to these contacts. 

Convergence is satisfied when either the ABSMAX or RELMAX condition is met. (Default: 

–9 

1.0×10 

) 

• DAMP is a number between 0 and 1.0 determining how quickly Tracer will converge on an 

open-contact solution using voltage biasing. The closer DAMP is to 1.0, the more quickly 

Tracer will converge, but there is also an increased chance of slower convergence due to 

overshoot. Usually the user should not be concerned with the value of DAMP. (Default: 0.9) 

• TRYCBC is used only if there is an open contact. Tracer will only attempt to use zerocurrent 

biasing when the current of the control electrode is greater than TRYCBC. Otherwise, 

voltage biasing is used. In most cases the user does not have to worry about this parameter. 

–17 

(Default: 1.0×10 

A/m) 

• ANGLE1, ANGLE2, and ANGLE3 are critical angles (in degrees) affecting the smoothness 

and step size of the trace. They are described in detail in [1]. If the difference in slopes of the 

Curve Tracer 243

Trace File 

last two solution points is less than ANGLE1, the step size will be increased for the next 

projected solution. If the difference is between ANGLE1 and ANGLE2, the step size remains 

the same. If the difference is greater than ANGLE2, the step size is reduced. ANGLE3 is the 

maximum difference allowed, unless overridden by the MINDL parameter. ANGLE2 should 

always be greater than ANGLE1 and less than ANGLE3. (Defaults: ANGLE1 = 5˚, 

ANGLE2 = 10˚, ANGLE3 = 15˚) 

• ITLIM is the maximun number of Newton loops for a given solution as specified in the 

method card of the PISCES input deck. The user should make sure that the value of ITLIM 

specified here is the same as that in the input deck. In certain cases, a PISCES solution may be 

aborted in Tracer because the solution will not converge within the given number of 

iterations. In some of these cases Tracer will try to redo the solution with a doubled number 

of iterations. If ITLIM is specified here, such attempts will be made. If there is no itlim 

statement or ITLIM=0, no attempts will be made. It is recommended that ITLIM be set to a 

low value, around 10 or 15 (or at least high enough to allow convergence of the initial 

solution). However, for GaAs devices a larger ITLIM of 20 or 25 is recommended. 

(Default: 0) 

• MINCUR is the value of the control current, in A/µm, above which Tracer carefully controls 

step size and guarantees a smooth trace. Below this current level, the program simply takes 

voltage steps as large as possible, i.e., as long as numerical convergence can be achieved, 

without regard for smoothness. If MINCUR is set to 0.0, Tracer will not begin smoothness 

control until it is past the first sharp turn in the I-V curve. This value should be used when the 

user is only interested in the rough location of a break in the curve, such as the breakdown 

voltage of a single-junction device. If smoothness is required, a lower value should be 

–15 

specified. Setting MINCUR below 1.0×10 A/ µ m is not recommended because Tracer has 

problems controlling smoothness at such low currents. (Default: 0.0A/ µ m) 

• MINDL is the minimum normalized step size allowed in the trace. Usually the user does not 

need to adjust this parameter. Increasing MINDL will reduce the smoothness of the trace by 

overriding the angle criteria, resulting in more aggressive projection and fewer simulation 

points. Reducing MINDL will enhance the smoothness and increase the number of points in 

the trace. (Default: 0.1) 

• FREQUENCY specifies how often the binary output (solution) files of the trace are saved. All 

I-V points are saved in outputfile. However, the PISCES solution files corresponding to 

these points are saved only if they are designated by FREQUENCY. If FREQUENCY=0, 

244 Curve Tracer

Trace File 

none of the solutions is saved, except perhaps the turning points (see below). If 

FREQUENCY=5, e.g., the solution file of every fifth point will be saved to files named soln.5, 

soln.10, etc., along with its PISCES input file (input.5, input.10,...) and output I-V file (iv.5, 

iv.10,...). (Default: 0) 

• TURNINGPOINTS is either YES or NO. If it is YES, the binary output (solution) file from 

PISCES will be saved whenever the slope of the I-V curve changes sign, i.e., there is a turning 

point. The name of the output file is soln.num,where num is the number of the current 

solution. For example, if the 25th point has a different sign than the 24th point, Tracer will 

save a file called soln.25. (Default: NO) 

• VERBOSE is either YES or NO. If it is YES, certain information about each solution (which 

the user may not be interested in) is printed in outputfile. The information consists of the 

external control-electrode voltage, the load resistance on the control electrode, the slope 

(differential resistance) of the solution, the normalized projected distance of the next 

simulation I-V point, and the normalized angle difference between the last two simulation 

points. (Default: NO) 


1. Step-size control will begin when the control electrode’s current exceeds 1.0×10 

A/µm. In the 

input deck itlim has been set to 12. Only essential information is saved in outputfile. The 

solution file of every tenth point, as well as any turning points, will be saved. 

option mincur=1e-14 itlim=12 verbose=no frequency=10 

+ turningpoints=yes 

2. In a simulation with one or two open contacts, we want to keep the current through the open 

–16 

electrodes below 1.0×10 

A/µm, regardless of the current through the control electrode. Thus 

RELMAX is set to a very low value so that it will not be a factor in determining the current at the 

open contact(s). 

option absmax=1e-16 relmax=1e-25 

–14 

Curve Tracer 245

Trace File 

9.4 SOLVE Card 


The solve card is used to specify how the initial solution is obtained, what simulator is used, and 

whether there are any open contacts (zero-current bias conditions). A Tracer run will start either with 

an initial solution or by loading a solution from a previous PISCES simulation. If such a previous 

simulation has one or two zero-current electrodes, the user has the option of either specifying the 

voltages on these electrodes or of simply designating them as open contacts. 

9.4.2 Syntax 

FIRSTSOLUTION= [OPENCONT1=] [OPENCONT2=] 

[SIMULATOR=] [VOPEN1=] [VOPEN2=] 


• FIRSTSOLUTION is either INITIAL, LOAD, or CURRLOAD. In all cases a solve 

statement should be present in the PISCES input deck (inputfile). The parameters of this 

solve card in inputfile are not used but rather the card itself is used to mark where a 

PISCES solve card should be placed by Tracer in inputfile (see SECTION 10). 

If FIRSTSOLUTION=INITIAL, a solution at thermal equilibrium will be solved by Tracer 

first. This implies that there cannot be any non-zero voltages or currents on a FIXED card. If 

the device has an open contact, i.e., a zero-current source, the user should not specify “current” 

on the contact line of the PISCES input deck to indicate a zero-current bias condition. 

Specifying OPENCONT1 or OPENCONT2 on the tracefile solve card is all that is 

needed. 

If FIRSTSOLUTION=LOAD, a load statement should be present directly above the solve 

card in inputfile, and it should designate the infile (see SECTION 10). This option is used 

if the trace is to begin from a previously generated input solution file. The simulation which 

created this solution file must have used only voltage bias conditions. An open-contact trace 

can still be generated from such an input solution file if the voltage bias condition on the open 

electrode(s) results in near-zero current for that electrode (see VOPEN1, VOPEN2 below). 

Such an open-contact case would most likely arise if the user wanted to extend a previous 

246 Curve Tracer

Trace File 

Tracer run in which voltage bias conditions were used on the zero-current electrodes for the 

last simulation point. 

If the loaded solution is from a simulation using a zero-current bias condition, 

FIRSTSOLUTION=CURRLOAD should be used. In this case “current” should be specified 

on a contact card for each open electrode. As in the FIRSTSOLUTION=LOAD case, the 

existing inputfile load card is used by Tracer, which means the correct “infile” should be 

specified on a load card directly above the solve card in inputfile. (Default: none) 

• OPENCONT1 and OPENCONT2 are the numbers of electrodes (between 1 and 9, inclusive) 

with a zero-current bias condition. There can be either zero, one, or two open contacts. When a 

device has an open contact, the user does not have to worry about convergence at low devicecurrent 

levels. Tracer will automatically adapt the bias conditions to guarantee convergence. 

(Default: none) 

• SIMULATOR is either PISC2ET (PISCES-2ET) or MD3200 or MD10000 (TMA). It 

designates the device simulator to be used by Tracer. Other additions may be made in the 

future. (Default: PISC2ET) 

• VOPEN1 and VOPEN2 must be used if and only if there is an open contact and 

FIRSTSOLUTION=LOAD (voltage bias condition on open contact(s)). The values of 

VOPEN1 and VOPEN2 are the voltages of the open contacts OPENCONT1 and 

OPENCONT2, respectively, in the loaded solution file designated on the load card of 

inputfile. If there is only one open contact, VOPEN2 should not be specified. (Defaults: 

0.0) 


1. The trace starts by solving an initial solution at zero bias and uses PISCES-2ET as the simulator. 

Electrode 2 is an open contact. 

solve opencont1=2 firstsolution=init simulator=pisc 

2. The trace starts with a previous solution using only voltage bias conditions. In this loaded solution 

the open contacts 2 and 4 have voltages of 0.641V and 0.509V, respectively. 

solve firstsolution=load simulator=pisc opencont1=2 

+ opencont2=4 vopen1=0.641 vopen2=0.509 

Curve Tracer 247

SECTION 10 

Input Deck Specifications 

The input deck used by Tracer, inputfile, is a standard PISCES file, but Tracer has certain 

requirements. For understanding the basic flow of an input deck, consult the PISCES manual. The 

mesh, region, electrode, doping, and model cards must already be present in the input deck. 

Additionally, the Newton solution method must be specified in the symbolic card. Other requirements 

are described below. 

10.1 Load and Solve Cards 

In Tracer, the user specifies whether to start with an initial solution or to load a previous solution (see 

Section 9.4). In either case, the user must mark a line in inputfile where the solve statement should 

go by starting the line with “solve”. Any parameter specified in this solve statement is irrelevant. If 

Tracer is to start with a previous solution, inputfile must contain a standard load statement, 

above the solve line, containing the name of the input file to be used (i.e., load infil=). In the case of loading a solution with a zero-current bias condition, “current” should be 

specified on a contact card for the open electrode. 

10.2 Contact Card 

Contact cards are optional in inputfile except in the case of electrodes biased with a current 

source. The case of the zero-current source is noted in Section 10.1 above. If there are any electrodes 

with a finite-current bias condition, a contact card with the “current” option should be placed in 

248 Curve Tracer

Input Deck Specifications 

inputfile for each such electrode, regardless of whether Tracer is to begin with an initial solution 

or a loaded solution. 

Even if no contact cards are required in inputfile, a line starting with “$contact” must be 

present so that Tracer will know where to add a contact statement. This contact card is necessary 

because this is where the load resistance of the control electrode is specified by Tracer. There is no 

problem with placing a contact card for the control electrode in the input deck as long as it does not 

specify a resistance value (which should never happen). Note that at least the first five letters of 

“contact” must appear for Tracer (and PISCES) to recognize it. 

10.3 Method Card 

In order to specify the maximum number of Newton iterations per solution, the itlim statement of the 

method card must be used in inputfile. If no method card is present, PISCES uses a default itlim 

of 20. However, in order to use the double-itlimit option (see Section 9.3), a method card must be 

present in the input deck and itlim must be set to some value. 

Another option must be specified in the method card if TMA’s MEDICI is used. In MEDICI, 

if a solution is aborted MEDICI will try to solve for an intermediate solution and then retry the original 

solution. This is not desirable when using Tracer since Tracer needs to keep track of aborted 

solutions. Thus, “stack=0” should be specified in the method card of MEDICI so that it does not 

attempt intermediate solutions. Analogously, the “trap” option should not be specified on the method 

card in a PISCES-2ET deck. 

10.4 Options Card 

When using PISCES-2ET, “curvetrace” should be specified on the options card so that PISCES will 

abort nonconverging solutions. Additionally, “nowarning” can be specified to prevent PISCES from 

printing warning messages which clutter the output, especially the warning issued when the load 

resistance changes value from one solution to the next. 

Curve Tracer 249

SECTION 11 

Data Format in Output Files 

As each solution is found, it is recorded in outputfile. Naming outputfile is described in 

SECTION 8. At the start of each line is the number of the solution. The second column of data contains 

voltage values of the control electrode, while the third column contains current values of the control 

electrode. If there is a zero-current electrode, the voltage and current values of OPENCONT1 will go 

in the next two columns, followed by the voltage and current of OPENCONT2 if there is a second 

open electrode. 

Values in the next columns depend on which data are recorded. If requested in the FIXED 

statements of tracefile, current values of fixed-voltage electrodes and voltage values of fixedcurrent 

electrodes will be recorded for each solution point in outputfile. The order from left to 

right is from low to high electrode number. 

After the electrode information is recorded, further columns contain information about each 

solution if VERBOSE=YES in the SOLVE card of tracefile. These columns are, from left to 

right, external control-electrode voltage, load resistance on the control electrode, differential 

resistance, normalized distance of the next projection, and the angle difference between the current and 

previous solution points (see [1] for a description of these parameters). 

The FREQUENCY and TURNINGPOINTS parameters in the OPTION card allow data to 

be saved for certain specified solutions. In outputfile, those points which are saved are marked 

250 Curve Tracer

Data Format in Output Files 

with an asterisk next to the solution number. The files saved are the input deck, input.i; the I-V data 

file, iv.i; and the solution file, soln.i; where i is the number of the solution in outputfile. 

Curve Tracer 251

SECTION 12 

Comments 

As of January 1994, Tracer works with PISCES-2ET, some in-house versions of Stanford PISCES, 

and to some extent md3200 or md10000, MEDICI Version 1.2.2. 1 Use of MEDICI is not yet robust 

and thus Tracer may or may not complete a trace using MEDICI. Also, MEDICI cannot yet be used 

for simulations with open contacts. Tracer has not been thoroughly tested for simulations with two 

open contacts. 

The capability to calculate admittances using the difference method must be added to Tracer 

if it is to use simulators which cannot perform AC analysis when a load resistor is present (a previous 

version has this capability, so it should not be hard to implement). 

A tar file has been created which contains the Tracer source code; an executable version of 

PISCES; this document in FrameMaker, MIF, and postscript formats; and a test suite of verified 

examples. This test suite contains all the files needed to run the examples in the appendix. 

1. These implementations were developed in connection with Advanced Micro Devices, where TMA 

software is used, as part of a summer internship. 

252 Curve Tracer

SECTION 13 

Examples 

In each of the Tracer examples below, a description of the simulation is given along with the 

command line used to invoke Tracer and figures with the listings of inputfile (the PISCES input 

deck), tracefile, and outputfile. 

13.1 BV CEO 

The BV CEO experiment is conducted by biasing an npn bipolar transistor’s collector positively with 

respect to the emitter while the base is left open. The PISCES input deck, bvceo.pis, shown in Figure 

13.1, defines the mesh, region, electrodes, doping, emitter contact, physical models, and solution 

method. Even though the contact card is not for the collector, which will be the control electrode, the 

presence of the card ensures that Tracer will be able to find the correct place to insert a contact card 

for the collector when it needs to. If we did not wish to use the contact card in bvceo.pis, we would 

still have to insert a line beginning with “$contact” above the model and symbolic cards. Notice that 

“nowarn” and “curvetrace” are specified on the options card and “newton” is specified on the symbolic 

card, while nothing is specified on the solve card. 

In the trace file bvceo.tra (Figure 13.2), the FIXED card sets the voltage on the emitter 

electrode (num=1, as defined by bvceo.pis) to a constant value of 0.0V and states that the current 

through this electrode will not be recorded in outputfile. Electrode 3, the collector electrode, is 

designated as the control electrode. The CONTROL card states that the first solution will have a 

Curve Tracer 253

Examples 

title NPN Simulation for Toshiba w/ coarse mesh (1/19/92) 

options nowarn curvetrace 

mesh rect nx=11 ny=12 

x.m n=1 l=0 r=1 

x.m n=4 l=0.7 r=0.65 

x.m n=11 l=2 r=1.2 

y.m n=1 l=0 r=1.0 

y.m n=3 l=0.2 r=0.7 

y.m n=7 l=0.4 r=1.0 

y.m n=12 l=2.5 r=1.3 


$electrode 1=emitter 2=base 3=collector 




dop ascii n.type infil=npn1.p x.l=0 x.r=2 ra=0.8 

dop ascii p.type infil=npn1.b x.l=0 x.r=2 ra=0.8 

dop ascii n.type infil=npn1.as x.l=0 x.r=0.6 ra=0.8 

dop gauss conc=1e18 p.type x.left=1.9 x.r=2 y.top=0 y.bot=0 

+ char=0.3 ra=0.8 

contact num=1 surf.rec vsurfn=8e5 vsurfp=8e5 

model temp=300 srh auger conmob fldmob bgn impact 

symbolic newton carr=2 

method itlimit=15 

solve 

end 

Figure 13.1 The input file bvceo.pis for the BV CEO example. 

254 Curve Tracer

Examples 

fixed num = 1 type=voltage value=0.0 record = no 

control num=3 begin=0.0 initstep=0.1 control=vmax end=20 

solve opencont1=2 first=init sim=pisc 

option verbose=no itlim=15 turnpts=yes freq=5 

+ mincur=5e-12 absmax=5e-19 

Figure 13.2 The trace file bvceo.tra for the BV CEO example. 

collector voltage of 0.0V, while the second solution will have a collector voltage of 0.1V. Tracing will 

continue until the collector voltage equals or exceeds 20V. If the initial step of 0.1V proves to be too 

large for convergence, Tracer will cut the step size in half, possible more than once, until it converges 

on a solution, and then will proceed from this solution. 

In the SOLVE card, we specify that the base electrode (num=2) is to be treated as an open 

contact during the trace. Also, tracing will begin with a thermal-equilibrium solution and PISCES- 

2ET will be used for the simulation. Finally, the OPTION card specifies that only essential I-V data 

will be saved in the output file; the PISCES iteration limit is set to 15, agreeing with the PISCES deck 

in the input file; PISCES solutions will be saved for any turning points as well as for every fifth 

solution point; smoothness of the I-V curve will not be enforced until the collector current is greater 

–12 

than 5×10 

A/µm; and while voltage biasing is used on the open base contact, a solution will be 

–19 

accepted only if the current through the base is less than 5×10 

A/µm (unless the RELMAX 

condition predominates). 

To run Tracer, the following command is typed at the prompt: 

machine-prompt% tracer bvceo.pis bvceo.tra bvceo.out 

While Tracer is running, the output of the PISCES runs are sent to the standard output, 

along with messages announcing when solutions are written to the output file. The output file, named 

bvceo.out in the command line, is shown in Figure 13.3, and a plot of the collector current vs. collector 

voltage is shown in Figure 13.4. In bvceo.out, we see that every fifth solution, along with solutions 24 

and 36 (the turning points), has been saved in files named soln.5, soln.10, etc. Additionally, the last 

solution was saved in the file soln.last, although there is no asterisk marking the last solution in 

bvceo.out. 

Curve Tracer 255

Examples 

Soln #Vctrl Ictrl Vcurr Icurr 

1 0.000000e+00 6.640216e-19 0.000000e+00 -1.365566e-18 

2 1.000000e-01 4.536067e-17 1.000000e-01 1.341435e-19 

3 3.000000e-01 1.625653e-14 2.519331e-01 1.110998e-19 

4 7.000000e-01 1.258870e-13 3.047182e-01 -1.057191e-19 

*5 1.500000e+00 5.969134e-13 3.445794e-01 -6.215285e-20 

6 3.100000e+00 9.010139e-13 3.543271e-01 3.507138e-20 

7 6.300000e+00 1.937138e-12 3.725358e-01 -2.823590e-20 

8 1.270000e+01 5.523255e-12 3.960896e-01 4.401873e-20 

9 1.303983e+01 7.789304e-12 4.048689e-01 7.261209e-20 

10 1.331971e+01 1.233772e-11 4.167027e-01 -2.392157e-20 

11 1.351640e+01 2.144845e-11 4.310039e-01 -3.015821e-20 

12 1.364322e+01 3.968015e-11 4.469627e-01 -2.586306e-20 

13 1.375854e+01 1.126228e-10 4.740828e-01 -3.055604e-20 

14 1.383613e+01 4.044189e-10 5.073686e-01 2.662945e-20 

15 1.389759e+01 1.571640e-09 5.427516e-01 -6.997169e-20 

16 1.395684e+01 6.240608e-09 5.787376e-01 4.017923e-20 

17 1.401870e+01 2.491678e-08 6.149198e-01 5.800187e-20 

18 1.408638e+01 9.962280e-08 6.512089e-01 2.496370e-19 

19 1.416639e+01 3.984529e-07 6.876080e-01 -7.339886e-20 

20 1.427994e+01 1.593805e-06 7.241677e-01 -1.364024e-19 

21 1.450307e+01 6.375431e-06 7.610238e-01 1.500092e-21 

22 1.508580e+01 2.550435e-05 7.985911e-01 1.631978e-19 

23 1.653961e+01 1.020878e-04 8.384486e-01 -8.203646e-20 

24 1.743830e+01 2.563710e-04 8.696470e-01 -1.839253e-19 

25 1.721139e+01 3.337692e-04 8.797490e-01 2.752857e-21 

26 1.608475e+01 4.874279e-04 8.953096e-01 -6.556564e-20 

27 1.467484e+01 6.389540e-04 9.070167e-01 4.997494e-19 

28 1.349730e+01 7.523351e-04 9.136248e-01 -3.868294e-19 

29 1.275292e+01 8.310109e-04 9.178346e-01 1.061968e-19 

30 1.208031e+01 9.464580e-04 9.248369e-01 7.411538e-21 

31 1.149536e+01 1.064806e-03 9.311878e-01 -4.402454e-19 

32 1.072725e+01 1.238428e-03 9.391391e-01 -1.234551e-19 

33 1.032238e+01 1.369005e-03 9.444611e-01 -5.772530e-19 

34 1.018224e+01 1.459092e-03 9.480149e-01 3.337310e-19 

35 1.012632e+01 1.578200e-03 9.526528e-01 5.859350e-19 

36 1.015785e+01 1.736090e-03 9.586154e-01 1.039733e-19 

37 1.033709e+01 2.050704e-03 9.697170e-01 3.375426e-19 

38 1.082413e+01 2.676637e-03 9.898170e-01 -5.421011e-20 

39 1.216369e+01 3.909572e-03 1.027822e+00 -3.201785e-19 

40 1.300269e+01 4.379769e-03 1.042119e+00 3.947174e-19 

41 1.372551e+01 4.658421e-03 1.050298e+00 -6.979551e-19 

42 1.482329e+01 4.950367e-03 1.058339e+00 1.677125e-19 

43 1.612039e+01 5.192516e-03 1.064355e+00 1.389134e-19 

44 1.757689e+01 5.415434e-03 1.068990e+00 -4.269046e-19 

45 1.886187e+01 5.634169e-03 1.071871e+00 -2.778268e-19 

46 2.017690e+01 6.057492e-03 1.073324e+00 6.572976e-19 

Figure 13.3 The output file bvceo.out for the BV CEO example. 

256 Curve Tracer

Examples 

Collector Current / amps/µm 

Collector Voltage / volts 

Figure 13.4 Collector current vs. collector voltage for the BV CEO example. 

At the top of bvceo.out, column headings mark the solution number, control-electrode 

(collector) voltage, control-electrode current, open-contact (base) voltage, and open-contact current as 

Soln, Vctrl, Ictrl, Vcurr, and Icurr, respectively. We see that the collector voltages for the first, second, 

and last solutions are 0.0, 0.1, and 20.18V, respectively. The final solution does not have a collector 

voltage of exactly 20V, as specified in bvceo.tra, because Tracer only guarantees that the curve will 

be traced out to at least 20V, not exactly 20V. 

Other information regarding the trace must be inferred from the PISCES output displayed 

while Tracer is running (not shown). From this output we can see that voltage biasing was used on 

Curve Tracer 257

Examples 

the open base contact for the first few solutions, in which the collector current is too small to allow 

stable use of zero-current biasing. A few PISCES simulations are actually run for each I-V point, with 

minor adjustments on the base voltage being made until the base current is less than ABSMAX. When 

the collector current is large enough, Tracer places a zero-current bias on the base. We can also see 

that a variable load resistor is placed on the collector when the collector current exceeds MINCUR. 

After this, the step sizes are regulated to produce a smooth curve. 

13.2 GaAs MESFET 

In this example, the drain of a GaAs MESFET is biased with respect to the grounded source with the 

gate set at -0.5V and the substrate grounded. Before Tracer can be used to sweep the drain electrode, 

a solution must be created, using PISCES-2ET, to set up the gate bias. The input deck shown in 

Figure 13.5 defines the device, finds the thermal-equilibrium solution, and then steps the gate bias to 

-0.5V while holding the other electrodes at 0V. The mesh and solution files are saved to the files 

mes.mesh and mesvg.5.ini, respectively. 

For Tracer, another PISCES input deck must be created to use as the input file (Figure 

13.6). In mesvg.5.pis the mesh file generated by mes.pis, mes.mesh, is read in, preempting the mesh, 

eliminate, region, electrode, and doping cards. Since Tracer will be starting with a previous solution, 

the name of the solution file to load must be given in mesvg.5.pis. This load statement appears directly 

above the solve card with the file name mesvg.5.ini, the solution file generated by mes.pis. 

The trace file mesvg.5.tra is shown in Figure 13.7. In the three FIXED cards, the voltages of 

the source and substrate (num=1 and num=4, respectively, as defined by mes.pis) have been fixed at 

0V, while the gate voltage (num=2) has been fixed at -0.5V. The current through the gate electrode 

will be recorded for each solution in the output file. The CONTROL card of mesvg.5.tra specifies that 

the drain (num=3) will be swept from 0.0V to a voltage where the current is greater than or equal to 

–4 

4.1×10 

A/µm, with an initial drain voltage step of 0.2V. On the SOLVE card, FIRSTSOLUTION 

is specified as LOAD, consistent with the input file mesvg.5.pis, and PISCES-2ET is designated as 

the simulator to use. Since VERBOSE is NO on the OPTION card, only the essential I-V data will be 

recorded in the output file. The iteration limit is 30, consistent with mesvg.5.pis, and every ninth 

solution, as well as those corresponding to turning points, will have its solution file saved. 

To run Tracer, the following command is typed at the prompt: 

machine-prompt% tracer mesvg.5.pis mesvg.5.tra mesvg.5.out 

258 Curve Tracer

Examples 

title mes.pis 

mesh nx=53 ny=41 rect diag.fli outf=mes.mesh 

x.m n=1 l=0 r=1 

x.m n=5 l=1 r=0.85 

x.m n=8 l=2 r=1.3 

x.m n=11 l=3 r=0.7 

x.m n=13 l=3.5 r=1 

x.m n=18 l=4 r=0.8 

x.m n=24 l=4.5 r=1.15 

x.m n=32 l=5 r=0.85 

x.m n=40 l=6 r=1.2 

x.m n=43 l=7 r=1 

x.m n=46 l=8 r=1.35 

x.m n=49 l=9 r=0.7 

x.m n=53 l=10 r=1.15 

y.m n=1 l=-.01 r=1 

y.m n=4 l=0.0 r=1 

y.m n=7 l=0.01 r=1 

y.m n=9 l=0.025 r=1 

y.m n=20 l=0.19 r=1 

y.m n=26 l=0.36 r=1.15 

y.m n=39 l=3.0 r=1.25 

y.m n=41 l=6.0 r=1.25 

elim y.dir iy.lo=1 iy.hi=3 ix.lo=1 ix.hi=4 












elim x.dir iy.lo=2 iy.hi=40 ix.lo=2 ix.hi=5 





Curve Tracer 259

Examples 

$*** regions 

region num=1 ix.lo=1 ix.hi=53 iy.lo=4 iy.hi=41 gaas 

region num=2 ix.lo=1 ix.hi=53 iy.lo=1 iy.hi=4 oxide 

region num=2 ix.lo=16 ix.hi=34 iy.lo=1 iy.hi=7 oxide 

$*** electrodes: 1=source 2=gate 3=drain 4=substrate 

elec num=1 ix.lo=1 ix.hi=5 iy.lo=1 iy.hi=4 




$*** doping 

dop ascii x.l=0.0 x.r=10.0 inf=mei.dop 

dop gaus x.l=-1 x.r=3.0 dos=5.0e13 cha=0.0607 peak=-0.0709 

+ n.t erfc.lat lat.cha=0.0866 

dop gaus x.l=7.0 x.r=11 dos=5.0e13 cha=0.0607 peak=-0.0709 

+ n.t erfc.lat lat.cha=0.0866 

$*** material 

material num=1 eg300=1.42 affinity=4.07 vsat=10.0e6 

+ permi=13.1 nc300=4.35e17 nv300=8.35e18 

interface qf=-1e12 x.min=0.0 x.max=10 y.min=-.01 y.max=6.0 

$*** contact 

contact num=2 alu workf=4.84 surf 

model conmob fldmob srh 

symb newton carrier=0 

method itlim=30 trap 

solve ini 


solve v2=-0.25 

solve v2=-0.5 proj outfil=mesvg.5.ini 

end 

Figure 13.5 Mesh generation file, mes.pis, for MESFET example. 

260 Curve Tracer

Examples 

title mesvg.5.pis 

option nowarn curvetrace 

mesh inf=mes.mesh 

material num=1 eg300=1.42 affinity=4.07 vsat=10.0e6 

+ permi=13.1 nc300=4.35e17 nv300=8.35e18 

interface qf=-1e12 x.min=0.0 x.max=10 y.min=-.01 y.max=6.0 

contact num=2 alu workf=4.84 surf 

model conmob fldmob srh hypert impact 


method itlim=30 

load infil=mesvg.5.ini 

solve 

end 

Figure 13.6 The input file mesvg.5.pis for the GaAs MESFET example. 


fixed num = 2 type=voltage value=-0.5 record = yes 


control num=3 begin=0.0 initstep=0.2 control=imax end=4.1e-4 

solve first=load sim=pisc 

option verbose=no itlim=30 turnpts=yes freq=9 

Figure 13.7 The trace file mesvg.5.tra for the GaAs MESFET example. 

Figure 13.9 shows the output file, mesvg.5.out, in which the solution number, drain voltage, 

drain current, and gate current have been recorded as Soln, Vctrl, Ictrl, and I2, respectively. The 

solution files of points 9, 18, 27, and 29 (a turning point), as well as of the last point (not marked in the 

output file) were saved as soln.9, soln.18, soln.27, soln.29, and soln.last, respectively. A plot of the 

drain current vs. drain voltage is shown in Figure 13.8. 

Curve Tracer 261

Examples 

Figure 13.8 Drain current vs. drain voltage for the GaAs MESFET 

262 Curve Tracer

Examples 

#Soln #Vctrl Ictrl I2 

1 0.000000e+00 1.903203e-16 -4.790550e-16 

2 2.000000e-01 4.411067e-05 -1.166555e-15 

3 6.000000e-01 1.233240e-04 -2.412571e-15 

4 1.400000e+00 1.985247e-04 -3.623966e-15 

5 3.000000e+00 2.104332e-04 -3.936303e-15 

6 4.600000e+00 2.155307e-04 -4.374722e-13 

7 6.200000e+00 2.189477e-04 -2.059647e-11 

8 7.000000e+00 2.202971e-04 -6.990150e-11 

*9 7.800000e+00 2.214088e-04 -1.707327e-10 

10 8.600000e+00 2.224028e-04 -3.638914e-10 

11 9.400000e+00 2.232137e-04 -6.557824e-10 

12 1.020000e+01 2.238725e-04 -1.043467e-09 

13 1.180000e+01 2.249711e-04 -2.208417e-09 

14 1.227965e+01 2.252584e-04 -2.671811e-09 

15 1.258651e+01 2.254261e-04 -2.980391e-09 

16 1.290104e+01 2.255882e-04 -3.308354e-09 

17 1.354587e+01 2.258872e-04 -3.995203e-09 

*18 1.441648e+01 2.262760e-04 -5.076190e-09 

19 1.517061e+01 2.266211e-04 -5.076190e-09 

20 1.818697e+01 2.280737e-04 -1.389891e-08 

21 3.025183e+01 2.340778e-04 -1.841648e-07 

22 3.326644e+01 2.357641e-04 -3.360147e-07 

23 4.526743e+01 2.472668e-04 -2.984657e-06 

24 4.787346e+01 2.524107e-04 -4.783998e-06 

25 5.085805e+01 2.612441e-04 -4.783998e-06 

26 5.436859e+01 2.808594e-04 -1.633647e-05 

*27 5.639889e+01 3.073427e-04 -2.612463e-05 

28 5.729060e+01 3.385567e-04 -3.460666e-05 

*29 5.719992e+01 3.725458e-04 -3.844234e-05 

30 5.586886e+01 4.090192e-04 -3.611460e-05 

31 5.534786e+01 4.193991e-04 -3.517154e-05 

Figure 13.9 The output file mesvg.5.out for the GaAs MESFET. 

Reference 

Curve Tracer 263

Examples 

[1] R.J.G. Goossens, S.G. Beebe, Z. Yu, and R.W. Dutton, “An Automatic Biasing Scheme for 

Tracing Arbitrarily Shaped I-V Curves,” IEEE Trans. on Computer-Aided Design, vol. 41, pp. 

310-317, March 1994. 

264 Curve Tracer

PART III 

Mixed-Mode Device/Circuit Simulator 

Francis M. Rotella, Zhiping Yu, and Robert W. Dutton


The prototype to the mixed-mode simulator was first developed in the summer of 1992 by Hui Wang, 

a visiting scholar from Tsinghua University, Beijing, China [1]. Funding for this project came from 

AASERT contract DAAH04-93-G-0178 on the parent Army contract DAAL03-91-G-0152. The 

MESFET example is provided by Matsushita Electric Industrial Co. in Japan and the GaAs/AlGaAs 

LED example is from OCD, HP, in San Jose, CA. 

Mixed-Mode Device/Circuit Simulator 265

266 Mixed-Mode Device/Circuit Simulator

CHAPTER 14 

Mixed-Mode Circuit and 

Device Simulation 

14.1 Introduction 

The Stanford mixed-mode interface provides a mechanism to include complex numerical devices in 

the SPICE circuit simulator when compact models are either inadequate or not available. Such devices 

include GaAs MESFET’s, heterostructure devices, short channel MOSFET’s, and optical devices. 

SPICE3f2 developed at UC Berkeley is used as the circuit simulator upon which the numerical device 

model is added. 

The mixed-mode simulator comes configured to work with Stanford’s version of PISCES-2ET. 

However, the modularity of the interface between SPICE and PISCES is such that any other device 

simulator may be interfaced with SPICE. Refer to “System Reconfiguration for a Different Device 

Simulator” on page 303 for more information. 

SPICE has many different types of analyses which Stanford’s mixed-mode simulator utilizes. 

Currently, a numerical device may be used in DC, AC small-signal, and transient analyses. Pole zero 

analysis has been included; however, this feature tends to have trouble in convergence for all but the 

simplest of circuits. Sensitivity analysis will be added in a later release. 


Mixed-Mode Circuit and Device Simulation 

14.2 Equations for Circuit Simulation 

A typical circuit simulator solves the non-linear circuit equations by a modified form of Newton- 

Raphson (NR) [2]. The non-linear system of equations for the circuit can be represented as shown in 

the following equation according to the Kirchoff’s current law: 

FV ( ) = 0 

(14.1) 

where V is the vector of node voltages and F represents the sum of the currents into each node in the 

circuit, and both V and F have dimension of N, the number of nodes in the circuit. 

Applying Newton-Raphson to the above equation yields the linear matrices shown in Equation 14.2 

where J( V) 

is the Jacobian as given in Equation 14.3. 

+ = V i – J – 1 ( V i )FV ( i ) 

V i 1 

(14.2) 

The index i is the iteration count during NR iterations. 

J( V) 

= 

∂F 1 ∂F 1 ∂F 1 

… 

∂V 1 ∂V 2 ∂ V N 

… … 

∂F N ∂F N ∂F N 

… 

∂V 1 ∂V 2 ∂ V N 

(14.3) 

For each Newton iteration, the previous voltage V i is known and hence V i + 1 can be computed. A 

circuit interpretation of Equation 14.2 and the Jacobian matrix (Equation 14.3) can be made as follows. 

Because each Jacobian element has units of the conductance, we hereafter use G to replace J. By 

multiplying G on both sides of Equation 14.2 from the left, one obtains the following set of linear 

equations at ( i + 1) 

-th iteration where i starts from 0: 

G i V i + 1 = G i V i – F i 

(14.4) 

The matrix G i and vector F i are evaluated at V i . The above equation represents a linear circuit as far 

V i + 1 

G i 

as node voltages because both the coefficient and the source term, i.e., the right hand side 

V i + 1 

G i 

(RHS) of the above equation, are independent from . Furthermore, can be interpreted as the 



linear conductance components, including both the linear components in the original circuit and 

differential conductance at V i , in the equivalent circuit. G i V i – F i can be viewed as the current 

sources. For a more detailed discussion, refer to McCalla [2]. 

The NR iteration is terminated when the convergence is reached, i.e., the change in V between two 

consecutive iterations is smaller than a predefined tolerance. In SPICE, it is required that the current 

change in each circuit branch is also below certain criterion when the convergence is considered to be 

reached. 

Transient analysis is performed in a similar manner. For each time step, Newton-Raphson iterations 

are performed until convergence is met. In addition, the truncation error due to the time discretization 

is checked to determine if the time step is acceptable in terms of accuracy. If this error is too large, the 

time step is reduced and the computation is repeated. 

For AC analysis, the DC solution is first sought and then the non-linear devices are linearized at the 

solution. This small signal equivalent circuit is used to find the AC response given an AC excitation 

vector. 

14.3 Equations for Device Simulation 

The details of the PISCES device simulator is discussed in Part I of this manual. This section discusses 

those details which are relevant to mixed-mode simulation. 

The device simulator is responsible for supplying the terminal currents and the admittance matrix at 

the given voltage boundary conditions. The device simulator first solves FwVt ( , , ) = 0 where 

w = f( ψ, n, 

p) 

for the drift/diffusion model and w = f ( ψ, n, p, T n , T p , T L ) for the duel energy 

transport model (see PART I) V is the terminal voltage on the device. From the solution, the terminal 

current density and conductance matrix can be calculated. For AC analysis, the admittance matrix must 

be calculated using frequency dependant AC analysis which is available in PISCES. 



14.4 Mixed-Mode Interface 

The mixed-mode interface is the code written at Stanford to provide the communication between 

SPICE and PISCES. Figure 14.1 shows how the two simulators are configured to talk with each other. 

Similarly to an analytic model (like a BJT or MOSFET), a numerical device is seen as just another 

block in SPICE. This block communicates to the numerical device simulator through an interface 

routine. Like other analytic models, the numerical device provides terminal currents (and 

conductances) for given node voltages. The difference is that the latter finds the solution numerically. 

This interface utilizes a two level Newton scheme to solve a circuit that includes numerical devices. 

On the upper level is the circuit iterations to determine the node voltages. For each one of these 

Circuit Simulator 

SPICE 

Analytic BJT Model 

Ic = F(Vbe,Vcb) 

Analytic MOS Model 

Id = F(Vgs,Vds,Vbs) 

Numerical Device 

Model 

Interface 

PISCES 

Device Simulator 

I = solution to semiconductor 

equations and models 

Figure 14.1 

Configuration of a numerical device model in the SPICE circuit 

simulator. 



SPICE 

Find Bias for 

Numerical 

Devices 

Write 


Simulator 

Input Deck 

PISCES-IIB 

PISCES-2ET 

Vendor PISCES 

Hal’s Simulator 

Execute 


Runs 

SPICE-TCAD 

Interface 

Execute 


Simulation 

Sockets 

TCP 

PVM 

TCL 

Load Device 

Simulation Results in 

G Matrix and I Vector 

Read 


Simulator Results 

PISCES-IIB 

PISCES-2ET 

Vendor PISCES 

Hal’s Simulator 

Figure 14.2 

Mixed-mode interface routines 

iterations, the device simulator solves for the terminal currents and conductance matrix using another 

Newton iteration within the device simulator (the lower level). The advantage of this method is the 

modularity created in the code. 

Figure 14.2 shows the flow diagram for the execution of a single iteration step at the upper level. The 

blocks on the far right hand side represents different modules for the device simulator and/or method 

of execution. The sequence of steps is as follows. 

1. Determine the voltage boundary conditions, time step, and/or frequency SPICE 

requires for the current iteration/solution. The exact information depends on 

the type of analysis. 

2. Create the numerical device input deck that solves for the information 

requested by SPICE. A separate module exists for each device simulator that is 

interfaced to SPICE. 



3. Execute the numerical device simulations on the current host or on a remote 

host by some specified protocol. 

4. Read the results of that simulation. 

5. Based upon the analysis type, load the SPICE conductance (admittance) matrix 

and current vector. 

6. Repeat for each device at each circuit iteration. 

Since a device simulation is required for each circuit iteration, the interface algorithms are given some 

intelligence to limit the computations required by the numerical device. The most important aspects or 

those algorithms are as follows: 

• Maintain files containing previous device solutions and utilize those 

solutions as a starting point for the requested bias. 

• Maximize the use of SPICE’s predictor corrector routines to decrease 

the calls to the device simulator. 

• Use a-priori knowledge of the device behavior to provide better guess 

of node voltages and to limit changes across pn junctions 

14.5 Computational Cost and Benefits 

The two level Newton method for mixed circuit/device simulation incurs a significant computational 

cost. Mayaram had investigated that cost for a variety of algorithms including the two level 

Newton [3]. The most common of the alternate algorithms is the full Newton which Rollins had 

implemented previously [4]. 

In the full level Newton algorithm, the circuit matrix and device matrix are combined into a single 

matrix and all variables are solved simultaneously. As a result, the computational time is reduced, but 

there are trade-offs. 

The two level Newton algorithm has the following advantages: 

1. It has better convergence for DC analysis if node voltages are unknown. The 

full Newton requires all circuit node voltages to be specified within a certain 

percentage; otherwise, it fails to converge. 



2. The modularity in two level Newton allows many device simulators to be used 

simultaneously. For example, PISCES may be used for standard devices in the 

circuit whereas an in house device simulator may be used for novel devices 

3. It is easier to implement a parallel version of the two level Newton algorithm. 

Each numerical device simulation can be relegated to a node of a parallel 

machine whereas the matrix for the full Newton algorithm has to be partitioned 

to each node. 

4. By utilizing SPICE as the circuit simulator, any improvements/modifications in 

SPICE automatically benefit the mixed-mode simulation. 

Likewise, there are a number of disadvantages to the two level Newton algorithm: 

1. Given a good estimate of all the circuit node voltages, the full Newton 

algorithm converges more quickly than the two level Newton. 

2. Similarly, since transient analysis involves small voltage changes at each time 

step making the problem well behaved, the full Newton method converges 

much more quickly for this case as well. Mayaram determined a factor of 1.7 

times as fast [3]. 

14.6 Parallelization 

In order to reduce the overall user time per circuit iteration, the numerical devices (i.e. the lower level 

Newton iterations) can be solve on different nodes on a network of machines. Because each device 

simulation is an independent unit, parallelization is relatively trivial. 

The mixed-mode interface contains two mechanisms by which the parallel simulations are executed. 

The most basic of these algorithms utilizes standard Unix sockets. A more elegant mechanism involves 

PVM (Parallel Virtual Machine) which allows a heterogenous network of computers to act like a 

parallel machine [5]. Figure 14.2 shows a block diagram of how PVM is utilized. 

The mixed-mode interface spawns a queueing process on a node of the virtual machine. This process 

ascertains the number of nodes that can be used for a device simulation. Whenever the interface 

program needs solutions from a number of numerical devices, it sends a request to the queueing 



Node 1 

Node 2 

SPICE 

Mixed-Mode 

Interface 

Queueing 

Controller 

for PVM 

Execution 

Node 3 

Sequential 

Execution 

Node 5 

Node 4 

Parallel 

Virtual 

Machine 

Figure 14.3 

Execution of the device simulations. 

program which then executes the device simulations on the available nodes. Once the device 

simulations are complete, the queueing program sends back the solutions to the interface. As a result, 

the computational load on the nodes is optimized. 


CHAPTER 15 

Use of Mixed-Mode Simulation 


The Stanford mixed-mode simulator provides a mechanism to incorporate numerical devices into a full 

circuit simulation with linear and non-linear components. The mixed-mode simulator uses the industry 

standard SPICE as the circuit simulator with an added model for the numerical device. This numerical 

model is configured modularly such that any device simulator may be added. (Refer to “System 

Reconfiguration for a Different Device Simulator” on page 303 for more information.) For the purpose 

of this document, Stanford PISCES is used. 

This chapter describes how to include a numerical model in a circuit simulation. All descriptions are 

based upon SPICE version 3f and hereafter referred to as SPICE only. 

15.2 New SPICE Cards 

Upon installing and configuring SPICE, the numerical model may be utilized in any circuit. The next 

two sections describe how to use the SPICE element card to specify the numerical device instance and 

the SPICE .model card for setting the parameters for the numerical device. The format for the cards 

is given in the SPICE manual notation [6]. 



COMMAND 

SPICE Element Card 

As with all element cards in SPICE, this card describes a specific instance 

of the numerical device in the circuit. The name of this instance is used as 

the predecessor for all files accessed in solving the specific numerical 

device. 

SYNTAX 

Nxxxxxxxx n1 n2 . . . nM mname 

+ 

PARAMETERS 

Nxxxxxxxx 

The N identifies the element type as being a numerical device and the x’s 

are used to represent a unique character string, which can be up to eight 

characters long, to identify the device. 

n1 n2 . . . nM 

The node numbers in the circuit to which the nM nodes of the numerical 

device are connected. They correspond in sequence to the electrodes of the 

device as specified in PISCES. There is a maximum limit of ten nodes per 

device. The voltage on any node is specified with respect to the last node as 

given by the nodes parameter on the .model card. 



mname 

The model name links this instance of the numerical device to the 

appropriate .model card. 

area 

The area or length factor for the device. All currents, capacitances, and 

conductances are multiplied by this value. The default is 1.0. 

off 

If off is specified, the DC operating point is determined with the terminal 

voltages for that instance of the device set to zero. 

ic 

These initial conditions for the device are used with the UIC specification 

on the .tran card. Each voltage initial condition is specified with respect to 

the last node. 

temp 

Operating temperature of the device. If none is given, the circuit 

temperature is used as the default. 

EXAMPLES 

Nbjt1 8 7 5 npndev 5 

This adds a numerical device with the name of Nbjt1 connected to circuit 

nodes 8, 7, and 5. These nodes correspond to electrode numbers 1, 2, and 3 

in the numerical device’s mesh. Electrode number 3 is taken as ground. 

Analogously with SPICE’s compact model for a bipolar junction transistor, 

Electrode 1 (Node 8) is the collector, Electrode 2 (Node 7) is the base, and 



Electrode 3 (Node 5) is the emitter. An area factor of 5.0 scales the device 

appropriately. 

Npn1 6 4 pndev area=6.5 ic=0.75 

This is a two node numerical device with circuit Node 6 corresponding to 

Electrode 1 and circuit Node 4 corresponding to Electrode 2. An initial 

condition of V 64 =0.75 V is placed on the device. The area is scaled by a 

factor of 6.5. 

BUGS 

The ic and off parameter have not been tested extensively. 

Some software paths have not been tested and may result in problems. 



COMMAND 

SPICE Model Card 

As with all .model cards in SPICE, this one is used to describe all 

instances of the same type. Common parameters are specified and used by 

all instances that reference the given model name. 

SYNTAX 

.model mname mtype nodes=ival [dtype=ival] [vto=rval] 

+ [model=ival] [method=ival] [vmax=rval] [vmin=rval] 

+ [hifreq=rval] [maxtrys=ival] [level=ival] [float=ival vbc=rval 

+ bcdep=ival] [oedev=ival] [tnom=rval] 

PARAMETERS 

mname 

Model name used for reference on the element cards. The mixed-mode 

interface expects to find certain files with this name as the predecessor to 

the file names. 

mtype 

The model type is given by a word mnemonic from Table 15.1. The 

mnemonic indicates the polarity of the numerical device and the 

mechanism by which the numerical simulation is executed. 

A plain pis device (independent of polarity) tells the mixed-mode interface 

to execute each of the numerical device runs sequentially on the same 

machine as SPICE. For the prl model, the mixed-mode interface uses 

UNIX sockets to execute each numerical simulation on a different machine. 



For the pvm model, the mixed-mode interface uses PVM message passing 

to send the biases to a queueing routine and ultimately a “slave” routine on 

a node of the parallel virtual machine. Refer to “Running a Mixed-Mode 

Simulation” on page 286 for more information. 

Table 15.1 

mtype 

pis 

npis 

ppis 

prl 

nprl 

pprl 

pvm 

npvm 

ppvm 

Description 

generic numerical device (default) 

n polarity numerical device (npn, nmos, pn junction) 

p polarity numerical device (pnp, pmos, np junction) 

generic numerical device simulated in parallel 

n polarity numerical device simulated in parallel 

p polarity numerical device simulated in parallel 

generic numerical device simulated using pvm 

n polarity numerical device simulated using pvm 

p polarity numerical device simulated using pvm 

nodes 

The number of numerical device nodes. This parameter defaults to 10 if no 

value is given. SPICE does not have a problem if this number is larger than 

the actual number of electrodes on the numerical device. The unidentified 

nodes are connected to ground by default. Likewise, one must be certain 

that the numerical device simulator can handle a “solve” statement with 

voltages specified for electrodes that do not exist. To avoid this problem, 

one should always specify this parameter. 

The nodes parameter may be less than the actual number of nodes in the 

numerical device. In this case, the extra nodes on the numerical device are 

considered floating and always ignored by the SPICE circuit simulator. 

Other .model parameters related to floating nodes include float, vbc, and 

bcdep. These parameters allow the user to switch boundary conditions on 

the floating node during a DC circuit solution. 



dtype 

This integer value provides SPICE with some a-priori knowledge of the 

device behavior. This parameter is not necessary, but is useful in achieving 

circuit convergence. Specifying a device type allows SPICE to make good 

guesses and limit voltage changes across pn junctions. The supported 

devices and their integer representations are configured in the NPISCdefs.h 

file. The default configuration is given in Table 15.2. The mtype parameter 

determines the polarity of the device. The electrode sequence for the 

electrodes is analogous to the SPICE compact model equivalents. 

Table 15.2 

dtype Description Electrode Sequence 

0 generic (default) does not matter 

1 BJT Collector Base Emitter Substrate 

2 MOSFET Drain Gate Source Bulk 

3 diode Anode Cathode 

4 MESFET Drain Gate Source Bulk 

5 LED Anode Cathode 

6 Inverter 

Psource Pgate Pdrain Ndrain Ngate 

Nsource Pbulk Nbulk 

7 Resistor Contact1 Contact2 Substrate (Cathode of diode) 

8 JFET Drain Gate1 Gate2 Source 

vt0 or vto 

This parameter represents the absolute value of the turn on voltage for the 

device. For a bipolar junction transistor it is Vbe on , for a diode it is Vd on , 

and for a FET it is Vgs on . The default value at room temperature is 0.7 V 

which is typical for a silicon pn junction. The polarity of the device model 

determines the sign. 



vmax 

This is the maximum voltage (in signed real number) placed on any 

numerical device electrode with respect to the reference electrode. The 

default value is 50.0 volts which one needs to increase for power devices. 

vmin 

This is the minium voltage (in signed real number) placed on any numerical 

device electrode with respect to the reference electrode of that numerical 

device. The default value is -50.0 volts. 

hifreq 

This value separates low and high frequency simulation of the numerical 

device. When the circuit frequency is below hifreq, the device’s small 

signal parameters are calculated from a zero frequency device simulation. 

When the circuit frequency is above hifreq, the device’s small signal 

parameters are calculated from a small signal device simulation at the given 

frequency. The trade-off is accuracy versus simulation time. The default 

value for hifreq is 1 kHz. 

maxtrys 

The maximum number of attempts the mixed-mode interface tries to get the 

device simulation to converge. Different bias stepping schemes are 

attempted with each try. 

level 

This integer represents a specific device simulator as defined in the 

NPISCdefs.h. Currently, the only one supported (and the default) is 

Stanford PISCES which is defined as level=0. This integer value 

determines how the method and model parameters are interpreted as well 

as the calling of the correct device simulator. More levels may be added 



so that other device simulators may be used in a mixed-mode simulation. 

Refer to “Adding Another Device Simulator” on page 311 for more 

information. 

model 

This is an integer value for the binary encoded representation of the model 

card in the device simulator input deck. The meaning of the integer value is 

described in the NUMDEVdefs.h file and interpreted by a routine 

specifically written for that device simulator. If this parameter is not 

specified and the file mname.model exists, the model card is taken as 

the content of that file. If neither is given, this card is not included in the 

input deck for the device simulator. Refer to “Running a Mixed-Mode 


method 

This is an integer value for the binary encoded representation of the method 

card in the device simulator deck. The meaning of the integer value is 

described in the NUMDEVdefs.h file and interpreted by a routine 

specifically written for that device simulator. If this parameter is not 

specified and the file mname.method exists, the method card is taken 

as the content of that file. If neither is given, this card is not included in the 

input deck for the device simulator. Refer to “Running a Mixed-Mode 


float, vbc, and bcdep 

These three parameters are used to control the boundary conditions on a 

floating node that can switch between a current and voltage boundary 

condition during DC analysis. This capability aids in the convergence of 

numerical devices with a floating node. At low currents in the device one 

uses a voltage boundary condition on the floating node and for high 



currents, one uses a current boundary condition on the floating node. The 

value of the voltage and current source on the floating node is zero. 

The parameter float contains the integer number for the floating node. It 

must be greater than the number specified by the nodes parameter. The 

parameter vbc determine the voltage at which the boundary condition is 

switched. The parameter bcdep specifies the positive and negative 

electrode on which the boundary condition depends. Refer to the examples 

for clarification. 

oedev 

An integer value of one for oedev tells SPICE that the numerical device 

will produce optical output. As a result, SPICE adds an equation to its 

circuit matrix to store the value of that output. In a future release, an integer 

value of two will tell SPICE that the numerical device has light incident 

upon it. The amount of incident light will be determined by referencing a 

circuit node. The default of zero means no photons are involved. 

tnom 

This parameter specifies the nominal temperature at which the parameters 

are given. Currently, the only parameter affected by tnom is vt0. The 

default value is 300K. 

EXAMPLES 

.model npndev npis vt0=0.7 dtype=1 model=93 method=336 

+ nodes=3 

This example defines the npndev model used in the previous example of 

an element card. This .model card tells SPICE that the npndev is of 

polarity n and that sequential simulations are executed for each instance of 

this model. The device type is a bipolar transistor as specified by the dtype 



parameter. The turn-on voltage for the device is 0.7 volts. The model and 

method for the device simulation is specified on the card and is explained 

in the next section. The number of nodes is given as three which 

corresponds to the three nodes on the previous element card. 

.model hpled ppis vt0=1.4 maxtrys=2 nodes=2 dtype=5 

+ float=3 vbc=1.0 bcdep=21 oedev=1 

This is a very complex model used for the simulation of an GaAs/AlGaAs 

LED with a floating layer. The turn-on voltage for the LED is 1.4 volts as 

defined by vt0. The number of nodes is two. The maximum number of 

tries for a given bias is limited to two. The floating node is electrode 

number 3 as given by the float parameter. The voltage boundary condition 

is used when V 21 is below 1.0 volts and the current boundary is used when 

V 21 is greater than or equal to 1.0 volts. The parameter bcdep specified 

V 21 as the controlling voltage and the parameter vbc specifies the voltage 

of V 21 when the boundary condition change is to takes place. 

In addition, this device will produce optical output and hence, an optical 

response. The model and method lines for the numerical simulator input 

deck is given in the files hpled.method and hpled.model. 

BUGS 

The advanced parameters for floating layers have been generalized, but 

may not be useful for all cases. 

When vmax and vmin are set stringently, they tend to cause SPICE to 

oscillate between the extremes. These parameters should be set such that 

they prevent the numerical device from entering breakdown. 

Some software paths have not been tested and may result in problems. 



15.3 Running a Mixed-Mode Simulation 

This section will describe how to set up a mixed-mode simulation using level=0 (Stanford’s version 

of PISCES). The first subsection describes the files the user must supply and those generated during 

the simulation. The next subsection describes the concept of the binary encoded method line and 

binary encoded model line. Finally, each of the different execution methods is addressed and the 

requirements for each is described. 

15.3.1 Files Required and Generated 

mynetlist.spi 

This file contains the circuit netlist of all the element cards and model cards for the circuit. Any valid 

SPICE construct is permitted. The name of the file can be arbitrary, but it is recommended that the 

extension .spi is used so that it may easily be recognized. 

mynetlist.raw 

The easiest way to run SPICE is to create a net list such that the circuit simulation is performed in batch 

mode. As a result, the user needs to save the solution SPICE computes. The name of the file can be 

arbitrary, but it is recommended that the extension .raw is used. To run SPICE in batch mode one 

types the following on the command line: 

spice3 -b mynetlist.spi -r mynetlist.raw 

Refer to the SPICE manual for more information [6]. 

mname.msh or mname.mesh.pis 

One of these files must be supplied to load or create the mesh during the PISCES simulation. The first 

is a standard PISCES mesh file. The second contains valid PISCES commands for creating the mesh 

from scratch. The mname corresponds to the model name given on the SPICE .model card. The 

extension .msh or .mesh.pis must be exactly as shown. The mixed-mode code first looks for 

mname.msh, if that file does not exist, it looks for mname.mesh.pis. If neither exists, SPICE 

aborts. 



Although these files are based on PISCES, they should be completely compatible and/or analogous for 

other device simulators. The actual format is determined by the programmer who adds the new device 

simulator. 

Using mname.msh provides for faster simulation because PISCES just loads the mesh and doesn’t 

have to create it each time. However, for some simulations, one may choose to create the mesh each 

time and therefore, the second option is available. When using mname.mesh.pis, the user should 

not include an end card. 

mname.model and/or mname.method 

These files contain the model and method cards for the PISCES input file, respectively. In writing an 

input deck, the mixed-mode interface should be given these cards. The binary encoded model and 

method parameters on the .model card in SPICE are the most efficient way to provide these cards 

without additional files or overhead. However, the encoding only accounts for logical variables; hence 

using the files provides a capability for including numerical variables on these PISCES cards. 

mname.soln.init 

This is a PISCES solution file containing the initial zero bias solution for the model mname. This only 

has to be found once for the model since all instances use the same starting point. 

Nxxxxxxxx.pis 

This file contains the PISCES input deck that the mixed-mode interface writes for the instance named 

Nxxxxxxxx. 

Nxxxxxxxx.out 

This file contains the output of the last PISCES simulation run for the specific instance. 

Nxxxxxxxx.soln.prev0, Nxxxxxxxx.soln.prev1, and Nxxxxxxxx.soln.prev2 

These files are generated by PISCES and contain the solutions for the specific instance at some 

previous bias. For DC analysis, the .prev0 file contains the solution for the current circuit iteration, 

the .prev1 file contains the solution for the previous circuit iteration, and the .prev2 file contains the 



solution for iteration before the previous. For transient analysis, .prev0 file contains the solution for 

the current time step, the .prev1 file contains the solution for the previous time step, and the .prev2 

file contains the solution for the time step before the previous time step. 

Nxxxxxxxx.log.ac and Nxxxxxxxxx.log.iv 

These files are generated by PISCES and contain the conductance/small signal parameters and the 

current vector respectively. 

hostname.pvm and hostname.prl 

These files are supplied by the user and contain a listing of hostnames if the mixed-mode simulator is 

used in a parallel configuration. Refer to “Types of Execution” on page 289 for more information. 

15.3.2 Method and Model Parameters 

The user may specify the binary encoded representation of the PISCES model card or PISCES method 

card on the SPICE .model line. This is accomplished by summing the numeral next to the appropriate 

action as given in the following tabulations. 

The binary encoded model parameter is computed as follows: 

+1 turns on srh 

+2 turns on consrh 

+4 turns on auger 

+8 turns on bgn 

+16 turns on conmob 

+32 turns on analytic 

+64 turns on fldmob 

+128 turns on surfmob 

+256 turns on impact 

+512 turns on ccsmob 

+1024 turns on fermi 

+2048 turns on incomplete 

+4096 turns on photogen 



The binary encoded method parameter is computed as follows: 

+1 turns off xnorm 

+2 turns on rhsnorm 

+4 turns on limit 

+8 turns on fixqf 

+16 turns on trap 

+32 turns on autonr 

+64 turns off 2nd 

+128 turns on tauto 

+256 turns off tauto 

+512 turns off l2norm 

+1024 turns of extrapolate 

For example, to generate the following model and method lines in the PISCES input deck, 

model consrh conmob bgn auger 

method trap ^2nd ^tauto 1 

the SPICE input file should contain a line similar to: 

.model fmrdev npis nodes=3 vt0=0.7 model=30 method=336 

15.3.3 Types of Execution 

There are three types of execution modes available to the user, but the compiled version of the 

mixed-mode code may not necessarily have all these capabilities. The type of execution is determined 

by the type of model given for the numerical device. 

pis, npis, and ppis 

This is the simplest of the possible models. A pis model sequentially executes the instances on the 

machine SPICE is executed. The minimum requirement is a SPICE netlist and a file containing the 

mesh. 

1. 2nd and tauto must be turned off for mixed-mode simulations using PISCES. 



prl, nprl, and pprl 

This type of model takes advantage of a network of computers. It uses standard UNIX sockets to 

execute the device simulations on remote hosts. The file system must be mounted on all these hosts 

with the same absolute path name. After a failure of maxtrys attempts, the parallel mode switches to 

the sequential mode for one attempt only. As a result, if a remote machine crashes or becomes 

unavailable for some reason, the mixed-mode simulation may not necessarily halt. 

The hostname.prl file contains a listing of the hosts on which the device simulations are executed. 

Each numerical device in the circuit is assigned a machine from the list and it is always executed on 

that machine. If there are more devices than machines then some machines can have more than one 

device executed on it. It is recommended that the machines be listed in decreasing computational 

power. 

The login and password for the remote machine is required. The mixed-mode code looks for the host 

name in the .netrc file. However, since the login and password for many hosts are the same, the user 

can use a machine name of “spice” in the .netrc file and the mixed-mode code uses that login and 

password for all hosts not found in the .netrc. 

pvm, npvm, and ppvm 

This type of model uses PVM to execute the numerical device simulations in parallel. PVM stands for 

Parallel Virtual Machine and may be obtained from netlib@ornl.gov. The user’s account must be 

configured for use with PVM as described in the manual and the user should have a working 

knowledge of PVM [5]. 

Three files are necessary for using PVM to execute a mixed-mode simulation. The user should place 

the executable files npiscctrl and npiscslave in the PVM bin directories of the appropriate 

machine architectures. In addition, hostname.pvm needs to contain a listing of all the nodes used 

for the mixed-mode simulation; however, they do not need to be added to the parallel virtual machine. 

If they are not in the parallel virtual machine, the mixed-mode simulator attempts to add them. 

Finally, the user should start and/or make sure that the PVM daemon is running on the local machine 

and then start the SPICE simulation. If the PVM daemon is not running, mixed-mode defaults to 

sequential execution. 


CHAPTER 16 

Examples 


This chapter describes examples using three types of analyses. The first is a CMOS inverter analyzed 

with a DC sweep on the input. The second is a GaAs MESFET analyzed for its high frequency 

response. The third is a six transistor SRAM cell analyzed through a read/write cycle. Another 

transient analysis is used to analyze a fiber optic transmitting circuit which includes a heterostructure 

LED with a floating layer. 

16.2 Single Stage CMOS Inverter (DC Analysis) 

This simple example demonstrates the basic capabilities of mixed-mode. The V out versus V in 

characteristics of a single CMOS inverter is simulated. Figure 16.1 shows the circuit schematic and the 

SPICE net list for the circuit. The two MOS transistors are numerical devices with electrode number 

1 being the drain, 2 the gate, 3 the source and 4 the bulk. 

For this simulation the mesh files for the two devices are created separately and are called 

fmrpmos.msh and fmrnmos.msh. These mesh files contain the grid and doping for the 

numerical device. The PISCES method and model options are chosen by the binary encoded SPICE 

parameters method and model as follows. 


Examples 

V dd (1) 

* cmos inverter example (DC analysis) 

vin 4 0 dc 0 

vdd 1 0 dc 5 

V in (4) V out (2) 

nm1p 2 4 1 1 fmrpmos area=5 

nm1n 2 4 0 0 fmrnmos area=2 

.model fmrpmos ppis dtype=2 vt0=0.8 model=94 method=336 nodes=4 

.model fmrnmos npis dtype=2 vt0=0.8 model=94 method=336 nodes=4 

Gnd (0) 

.dc vin 0 5 0.1 

.end 

Figure 16.1 

CMOS inverter circuit schematic and netlist. 

method ^2nd ^tauto trap 

model consrh auger bgn conmob fldmob 

For the DC analysis, the input voltage is swept from zero volts to five volts and the output voltage and 

supply current are monitored. The output waveform is as what would be expected from a CMOS 

inverter and is not shown. 

16.3 High Frequency GaAs MESFET (AC Analysis) 

The analysis of the GaAs MESFET mixed-mode simulation consists of finding the S-parameters of the 

two port network shown in Figure 16.2. SPICE can not directly find the S-parameters; however, it can 

easily find the Y-parameters with an AC perturbation applied to one input while the other is shorted. 

Two SPICE net lists are created, mes1.spi and mes2.spi. One perturbs port 1 of the network and 

the other perturbs port 2; hence each provides Y*1 and Y*2 respectively. One of the netlists is shown 

in Figure 16.2. 

For this simulation, the file mes.mesh.pis contains the PISCES cards for creating the MESFET’s 

mesh during each device simulation. Note that nothing specific has to be written in the SPICE netlist 


Examples 

I gate 

+ 

MESFET 

I drain 

+ 

V gate 

V drain 

- 

- 

* MESFET circuit 

vgg 9 0 dc 0.0 ac 1 

vdd 10 0 dc 2.0 

vgate 9 8 0 

vdrain 10 1 0 

ld 1 2 0.08n 

rd 2 3 1.52 

cd 2 0 212f 

lg 8 7 0.105n 

rg 7 4 0.92 

cg 7 0 208f 

ls 0 6 0.005n 

rs 6 5 1.38 

nm1 3 4 5 0 mes area=100 

.model mes npis vto=1 maxtrys=10 nodes=4 dtype=4 

.ac lin 40 1G 40G 

.end 

Figure 16.2 

Two port network and netlist for AC analysis to find the 

Y-parameters 

to differentiate using a previously created mesh file. In addition, the files mes.model and 

mes.method are also supplied and each contains one of the following lines respectively. 

model conmob fldmob srh hypert impact 

method trap ^2nd ^tauto itlim=30 


Examples 

* S11 

x S22 

Figure 16.3 

S-parameters for GaAs MESFET in the frequency range of 1GHz 

to 40GHz. 

An AC analysis is performed at each input of the two port network with other shorted. The 

Y-parameters are calculated by taking the currents I gate and I drain and dividing by the AC excitation 

magnitude. A simple transformation yields the S-parameters for a 50 ohm cable. The results are 

displayed in Figure 16.3. 

16.4 SRAM Cell (Transient Analysis) 

This example shows a circuit simulated with transient analysis and utilizing a network of computers. 

Figure 16.4 shows the circuit diagram for the SRAM circuit. The shaded region is the six transistor 

SRAM cell and is simulated using numerical MOS devices. The unshaded region is the control 

circuitry and is simulated with MOS level 2 compact models. 

The transient analysis of the circuit consists of a write and read cycle. The output of the flip-flop and 

the data lines are observed. Figure 16.5 contains the net list for the circuit. There is an extra compact 

NMOS transistor for leveling the charges of the data line capacitances. After a read or write cycle, this 


Examples 

VDD 

C 

L 

L 

C 

R 

WB 

WB 

CS 

CS: Selects appropriate column 

R: Selects appropriate row 

Read: 

Write 1: 

Write 0: 

Output: 

CS high, R high, WB low, WB low 

CS high, R high, WB high, WB low 

CS high, R high, WB low, WB high 

Measured across CC 

Figure 16.4 

Simplified circuit diagram of SRAM cell including control 

circuitry. 

transistor turns on to allow the charge between the data lines to distribute evenly. The data lines must 

be equal before anymore actions can take place. 

The models for the numerical devices are the same as those used for the CMOS inverter. The compact 

model is SPICE Level 2 model which closely represents the numerical model. The devices in the 

circuit are not the state-of-the-art, but they do provide a good example. The SPICE .nodeset line is 


Examples 

* supply line 

Vdd 1 0 5 

* the cell itself 

NM1 4 5 1 1 fmrpmos area=2 

NM2 5 4 1 1 fmrpmos area=2 

NM3 4 5 0 0 fmrnmos area=4 


* estimated parasitic of the cell 

Ci1 5 0 0.01p 

Ci2 4 0 0.01p 

* pass gates 



* control lines 

M7 1 1 2 0 ndev l=2u w=25u 

M8 1 1 3 0 ndev l=2u w=25u 

M9 2 9 6 0 ndev l=2u w=25u 

M10 3 8 6 0 ndev l=2u w=25u 

* access line 

M11 6 10 0 0 ndev l=2u w=50u 

* level line 

M12 2 12 3 0 ndev l=2u w=25u 

* estimated load on lines 

Crow 7 0 0.5pf 

Ccol 2 0 2pf 

Ccolb 3 0 2pf 

* access control sources 

VCS 10 0 pulse(0 5 0.2n 0.2n 0.2n 8n 20n) 

VR 7 0 pulse(0 5 0.2n 0.2n 0.2n 8n 20n) 

* data control sources */ 

VWBb 8 0 pulse(0 5 40.2n 0.2n 0.2n 8n 80n) 

VWB 9 0 pulse(0 5 0.2n 0.2n 0.2n 8n 80n) 

Figure 16.5 

SPICE netlist for SRAM simulation. 


Examples 

* data line level sources 

VL 12 0 pulse(0 5 9n 0.2n 0.2n 8n 20n) 

.nodeset v(5)=0 v(4)=5 v(2)=3.5 v(3)=3.5 

.tran 0.1n 40n 

* compact models 

.model pdev pmos 

+ level = 2.000 vto = -0.5677 gamma = 0.51 

+ phi = 0.73 tox = 2.5000E-08 nsub = 4.0251E+14 

+ nfs = 6.8412E+11 xj = 2.5976E-8 ld = 1.8553E-07 

+ uo = 1.705E+02 ucrit = 2.2295E+05 uexp = 0.2918 

+ vmax = 6.8950E+04 neff = 9.285E+1 delta = 0.5587 

+ cj = 2.7923E-04 cjsw = 2.1805E-10 pb = 0.7316 

+ mj = 0.4729 mjsw = 0.2195 fc = 0.5 

+ cgdo = 4.71e-10 cgso = 4.71e-10 

.model ndev nmos 

+ level = 2.000 vto = 0.6000 gamma = 0.4500 

+ phi = 0.6000 tox = 2.5000E-08 nsub = 1.6300E+15 

+ nfs = 3.0000E+11 tpg = 1.000 xj = 3.5000E-07 

+ ld = 1.0000E-07 uo = 612.0 ucrit = 2.0000E+05 

+ uexp = 0.2500 vmax = 5.8000E+04 neff = 45.00 

+ delta = 3.900 cj = 1.4620E-04 cjsw = 3.1626E-10 

+ pb = 0.6495 mj = 0.3640 mjsw = 0.2558 

+ fc = 0.5000 cgdo = 4.39e-10 cgso = 4.39e-10 

* numerical devices 

.model fmrpmos npvm dtype=2 vt0=0.8 model=94 method=336 nodes=4 

.model fmrnmos npvm dtype=2 vt0=0.8 model=94 method=336 nodes=4 

Figure 16.5 

Continuation of SPICE netlist for SRAM simulation. 

used to set the flip-flop to an initial state rather than having it start indeterminately. The .tran card 

specifies the limits of the transient analysis. 

The numerical device models are specified as pvm. As a result, each numerical device simulation is 

executed on a different node of a parallel virtual computer. The file hostname.pvm is provided 

with a list of hostnames for the nodes. The network uses a common file server whose disks are mounted 

on each of the remote hosts. 


Examples 

Data Lines 

5 

4 

3 

2 

1 

0 

C 

C 

Latch 

5 

4 

3 

2 

1 

0 

L 

L 

Read/Write Cycle 

Figure 16.6 

5 

4 Write 1 

Read 1 

3 

2 

1 

0 

0 5 10 15 20 25 30 35 40 

Time (ns) 

Read/Write cycle for SRAM cell. 

Figure 16.6 shows the output waveforms of the SRAM cell. It is important to note how fast the 

difference between the data lines becomes small. This time determines the minimum read/ write cycle 

time. 

16.5 GaAs/AlGaAs LED (Transient Analysis) 

This final example involves a device with a floating node. Figure 16.7 shows the cross section of the 

cylindrical LED. The cathode contact is electrode number 1, the anode contact is electrode number 2, 

and the floating layer is electrode number 3. In order to improve convergence in the device simulation, 

the floating layer must switch from a voltage boundary condition to a current boundary condition when 

high currents are flowing. Refer to the paper by Dutton for a detailed discussion [7]. 


Examples 

cathode 

contact 

emitted light 

floating 

layer 

n+ 

n 

n 

p 

p 

anode 

contact 

Figure 16.7 

Cross section of LED structure that is used in a fiber optic 

transmitter circuit. 

At low currents and biases, the voltage boundary condition introduces some error, but it is tolerable 

since that is not the range of interest for the operation of the device. For higher currents, the node is 

kept floating by placing a current boundary condition with a current source value of zero. In order to 

handle this switching, there are three special parameters. 

This device is placed into the transmitter circuit shown in Figure 16.8. The purpose of this circuit is to 

take an ECL signal, convert to TTL, and either turn on or off the LED. The SPICE netlist for the circuit 

is also given. 

First, one notes that this device is called using ppis model because a ppis device is defined such that 

the cathode is electrode 1 and the anode is electrode 2. An npis device has the reverse. In general, the 

n-polarity devices are such that the device is in its SPICE standard forward operating state. 


Examples 

+5 V 

Vcc 

0.1 µF 

10 µF 

33 Ω 

33 Ω 

TTL 

in 

56 µF 

270 Ω 

* driver circuit for HP transmitter 

* supply 

Vcc 6 0 DC 5 

Vin 1 0 pulse(5 0 1n 1.2n 1.2n 20n 40n) 

Rin 1 2 1 

* driver circuit 

R8 2 3 33 

C4 2 3 75p 

R9 3 4 33 

r10 4 0 270 

Vhp1 6 5 DC 0 

nhp1 4 5 hpled 

.options abstol=1e-9 

.model hpled ppis vt0=1.4 maxtrys=2 nodes=2 dtype=3 float=3 

+ vbc=1.0 bcdep=21 

.tran 100p 40n 0 200p 

.end 

Figure 16.8 

Circuit schematic and netlist for LED transmitter simulation. 

The rest of the parameters on the .model line are set to account for the heterostructure device. vt0 is 

set to turn on the device. The maxtrys parameter limits the maximum number of tries to two. This 


Examples 

parameter is set low because the cutting of the bias step does not take into account a changing boundary 

condition. The number of nodes is set to the actual number of contacts in the SPICE circuit. The 

floating node is not connected to anything and hence, SPICE does not need to know about its existence. 

The three parameters float, vbc, and bcdep specify the node and the switching point for the boundary 

condition.The floating node is electrode number 3 as given by the float parameter. The voltage 

boundary condition is used when V 21 is below 1.0 volts and the current boundary is used when V 21 is 

greater than or equal to 1.0 volts. The parameter bcdep specifies V 21 as the controlling voltage and 

the parameter vbc specifies the voltage of V 21 when the boundary condition change is to take place. 

The device uses cylindrical coordinates and hence, the area factor is allowed to default to 1.0. The 

mesh is created each time the device is solved because the version of PISCES being used can not save 

the heterostructure parameters. Hence, the file hpled.mesh.pis must be supplied. In addition, the 

model and method cards are given in the files hpled.model and hpled.method and are as 

follows. 

models fldmob auger conmob rad consrh 

method itlim=50 p.tol=5.e-5 c.tol=5e-5 ^2nd ^tauto 

A communications circuit engineer is most interested in the turn-on turn-off characteristics of the 

diode. Therefore, the transient simulation consists of a pulse input to switch the diode on and back off. 

The TTL nand gates used for supplying the current are substituted with a voltage source and a resistor. 

The voltage source takes into account the finite rise and fall time of the nand gates while the resistor 

simulates the output resistance of the nand gate. 

Figure 16.9 shows the response of the diode. This current is directly related to the amount of photons 

out for the device. 


Examples 

120 

100 

80 

60 

I hp1 (mA) 

40 

20 

0 

-20 

-40 

-60 

0 5 10 15 20 25 30 35 40 

Time (ns) 

Figure 16.9 

Time transient response of the current flowing through LED in a 

transmitter circuit. 


CHAPTER 17 

System Reconfiguration for a 

Different Device Simulator 

17.1 Changes in SPICE 

This chapter addresses the changes needed in SPICE so that a numerical device simulator may be 

added to the in-house version of SPICE. These instructions are based upon the 3f release of SPICE. 

The configuration for the 3e release is unknown at the writing of this manual. The 3d release has a 

slightly different configuration and those differences are described in this chapter. In order to configure 

3e or 3c release of SPICE, the administrator can use the descriptions in this chapter and also refer to 

the SPICE software documentation [8][9]. 

When referring to a directory, the home directory is to be taken as spice3f/src unless otherwise 

specified. 


System Reconfiguration for a Different Device Simulator 

17.1.1 New Files 

Table 17.1 contains a manifest of files needed for including the numerical devices. 

Table 17.1 

inp2n.c makedefs npisc.c 

npiscacload.c npiscask.c npiscconvtest.c 

npiscctrl.c npiscdefs.h npiscdelete.c 

npiscexec.c npiscexecprl.c npiscexecpvm.c 

npiscexecseq.c npiscgethost.c npiscgetic.c 

npiscitf.h npiscload.c npiscmdelete.c 

npiscmethod.c npiscmodel.c npiscmparam.c 

npiscmvfiles.c npiscparam.c npiscpvmmesg.c 

npiscpzload.c npiscreadpvm.c npiscreadstanford.c 

npiscsetup.c npiscslave.c npisctemp.c 

npisctrunc.c npiscwritestanford.c numdevdefs.h 

makefile.3d2 

These are subject to change for later versions, but differences should not be significant. 

17.1.2 Steps for Adding Numerical Devices to SPICE 

1. In bin/config.c there are two sets of include statements for the devitf.h 

files. Add each of the following lines to the appropriate list. 

#include “npiscitf.h” 

#include “npisc/npiscitf.h” 

2. Also in bin/config.c, there is a series of #ifdef structures to which one adds 

the following. 

#ifdef DEV_npisc 

&NPISCinfo 

#endif 



3. In include/inpdefs.h, there are two listings for the routines that are used 

to read an individual SPICE device type. The following lines are added to the 

appropriate list. 

void INP2N( GENERIC*, INPtables*, card* ); 

void INP2N(); 

4. The following line is added to the subroutine inp_numnodes() in lib/fte/ 

subckt.c. The number that is returned is the maximum number of nodes that 

the numerical device can support. 

case: ‘n’: return(10); 

5. Add the file inp2n.c to the directory lib/inp. Modify the makedefs file 

in that directory to include inp2n.c in the CFILES definition and to include 

inp2n.o in the COBJS definition. Finally, add the following entry to the list 

of files to make. 

inp2n.o: inp2n.c 

6. The following lines are added to lib/inp/inpdomod.c. These are the valid 

model types available for a numerical device. The administrator can eliminate 

an execution method by not including it in this listing. 

} else if ( (strcmp(typename,”pis”) == 0) || 

(strcmp(typename,”npis”) == 0) || 

(strcmp(typename,”ppis”) == 0) || 

(strcmp(typename,”pvm”) == 0) || 

(strcmp(typename,”npvm”) == 0) || 

(strcmp(typename,”ppvm”) == 0) || 

(strcmp(typename,”prl”) == 0) || 

(strcmp(typename,”nprl”) == 0) || 

(strcmp(typename,”pprl”) == 0) ){ 

type = INPtypelook(“Npisces”); 

if (type < 0) { 

err=INPmkTemp(“Device type Npisces not available in this binary\n”); 

} 

INPmakeMod(modname,type,image); 



7. The following line identification is added to lib/inp/inppas2.c 

case ‘N’: 

INP2N(ckt,tab,current,gnode); 

break; 

8. Make the directory lib/dev/npisc and copy all the files into this directory 

except for inp2n.c which should be placed in lib/inp. 

9. In the main configuration file, one needs to include “npisc” in the listing of 

devices to compile. This configuration file is located in the conf directory 

which is at the same level as the src directory. 

10. The user should clean everything and recompile SPICE. There may be 

dependencies that are not taken into account when certain header files are 

modified. 

17.1.3 Increasing Number of Nodes for a SPICE Device 

The released version of SPICE is configured for five nodes per device. For numerical devices, the 

maximum number of nodes is set to ten (This number corresponds to the maximum number of 

electrodes that Stanford PISCES allows). Because of the way new devices are interfaced to SPICE, the 

number of device nodes is set in the code. Fortunately, expanding the number of nodes is trivial [9]. 

1. Modify the file lib/ckt/cktbindn.c to include the cases for nodes six 

through ten. Follow the pattern already prescribed for nodes one through five. 

2. Modify the file include/gendefs.h to include the additional nodes six 

through ten in the pattern prescribed by nodes one through five. 

3. The user should clean everything and recompile SPICE from scratch. There 

may be dependencies that are not taken into account when certain header files 

are modified. 

17.1.4 Configuring NPISC for Use with PVM 

In order to use PVM to execute a device simulation, the following changes are implemented. These 

changes configure the routines that access PVM and compile the slave processes. PVM 3.0 or higher 

is assumed to be installed on appropriate machines and a working knowledge of PVM is assumed [5]. 



1. In the conf/defaults define the variable PVM_DIR to the PVM home 

directory. For example: 

PVM_DIR = /home/spice/pvm3 

2. For each specific architecture file define the variable PVM_ARCH to the 

correct PVM bin directory. For example, in the conf/sun4 file one includes 

the following line. 

PVM_ARCH = SUN4 

In addition, the following variables are also defined in the individual 

architecture configuration files. 

PVM_BIN = $(PVM_DIR)/bin/$(PVM_ARCH) 

PVM_TYPE = PVM_PUBLICDOMAIN 

The PVM_TYPE variable is included so that other version of PVM can used. 

For example, IBM has their own version of PVM. If the mixed-mode code is 

changed to include this version, all changes should be enclosed by an #ifdef 

structure using a new name for PVM_TYPE. 

3. Copy (or link) the files npiscslave.c and npiscctrl.c to the directory 

src/bin. 

4. The makedefs file in the directory src/bin has the following lines added 

so that the npiscslave and npiscctrl routines are compiled and installed 

correctly. In the list of CFILES, add the files npiscslave.c and 

npiscctrl.c. In the list of INSTALL_TARGETS add the following lines. 

$(PVM_BIN)/npiscslave \ 

$(PVM_BIN)/npiscctrl 

A variable COBJS is defined below CFILES as follows. 

COBJS = npiscslave.o npiscctrl.o 

Finally, add the following line to the list of object files. 

npiscslave.o: npiscslave.c 

npiscctrl.o: npiscctrl.c 



5. The makeops file in the directory src/bin is modified to include the 

following lines. Around line number 14 add the following. 

$(PVM_BIN)/npiscslave: npiscslave 

rm -r $@ 

cp $? $@ 

$(PVM_BIN)/npiscctrl: npiscctrl 

rm -r $@ 

cp $? $@ 

Around line number 55 add: 

npiscslave.o: npiscslave.c 

$(CC) -c $(CFLAGS) -I$(PVM_DIR)/include \ 

-I$(SRC_DIR)/../lib/dev/npisc \ 

-D$(PVM_TYPE) \ 

$(SRC_DIR)/npiscslave.c 

npiscctrl.o: npiscctrl.c 

$(CC) -c $(CFLAGS) -I$(PVM_DIR)/include \ 

-I$(SRC_DIR)/../lib/dev/npisc \ 

-D$(PVM_TYPE) \ 

$(SRC_DIR)/npiscctrl.c 

In the LIBS declaration around line number 150 add the following to include 

the PVM library: 

$(PVM_DIR)/lib/$(PVM_ARCH)/libpvm3.a 

Finally, around line 160, add the following compilations: 

npiscslave: npiscslave.o $(OBJ_TOP)/lib/dev.a \ 

-@rm -f npiscslave 

$(CC) -o $@ npiscslave.o $(OBJ_TOP)/lib/dev.a \ 


npiscctrl: npiscctrl.o $(OBJ_TOP)/lib/dev.a \ 

-@rm -f npiscctrl 

$(CC) -o $@ npiscctrl.o $(OBJ_TOP)/lib/dev.a \ 




17.1.5 Different Versions of SPICE 

There are some difference between SPICE3f and SPICE3d. This section attempts to clarify as many 

of those differences as possible; however, it may not be all inclusive and it does not include the changes 

for configuring the compilation for use with PVM. For versions other than 3f and 3d the administrator 

should refer to the implementation guides [8][9]. In addition, the BJT device provides an excellent 

basis for how a new SPICE device is installed. 

The first and most obvious difference is that SPICE3d capitalizes the identifier of each module. As a 

result, anywhere npisc is specified, it becomes NPISC. For example npiscload.c becomes 

NPISCload.c and DEV_npisc becomes DEV_NPISC. 

Following are the differences between SPICE3f and SPICE3d given in the same sequence as the 

original installation instructions. 

1. Instead of changing the bin/config.c file, one needs to make the given 

change in the bin/spice.c file. 

2. Instead of changing the bin/config.c file one needs to make the change in 

the include/devices.h file. 

3. Instead of changing the include/inpdefs.h file, one needs to make the 

change in the include/INPdefs.h file. 

4. One needs to change the lib/FTE/subckt.c file instead of the lib/fte/ 

subckt.c file. 

5. The file INP2N.c should be added to the lib/INP directory and the 

appropriate change should be made to the Makefile in that directory. 

6. Change the lib/INP/INPdomodel.c instead of the lib/inp/ 

inpdomod.c file. 

7. Add the new line to lib/INP/INPpas2.c instead of lib/INP/INPpas2.c. 

8. The directory for the numerical device is called lib/DEV/NPISC, the files 

should have “npisc” changed to “NPISC”, and makefile.3d2 is renamed to 

Makefile. In addition, there are a few changes to the code as outlined here. 

First, the include filenames need to be changed since SPICE3d uses a different 



naming convention as described previously. Second, NPISC.c and 

NPISCitf.h are not in the correct form. The user should examine BJT.c and 

BJTitf.h for reference, but the following paragraphs point out the changes 

that are required. 

In NPISC.c, the variables NPISCiSize and NPISCmSize are defined for the 

size of the instance and model. SPICE3d does not use these variables and 

consequently, they should be removed from the file. Likewise, in NPICSitf.h 

the extern lines for these variables should be removed and the other reference 

to these variables should be replaced with an explicit sizeof() statement. The 

code may work if these variables are in the code, but it has not been tested. 

Also in NPISCitf.h, there is an #ifdef DEV_npisc statement surrounding the 

code. This statement and the corresponding #endif at the end of the code 

should be removed. 

SPICE3f has a location for an additional function called DEVunsetup. This 

function is not in SPICE3d and is not used by the DEVice NPISC. Therefore, 

this line is removed from the function list in NPISCitf.h. This function is 

defined as NULL, between the two definitions for NPISCsetup. Refer to the 

BJTitf.h file for a comparison. Also in NPISCitf.h, there is a line DEV 

DEFAULT which is deleted. Finally, in NPISCdefs.h, the NPISCstate 

variable in the NPISCinstance structure is moved from its location at the 

beginning and placed at the end of the structure. SPICE3f requires it to be there 

while SPICE3d requires it not be there. 

If SPICE3d does not work correctly after making these changes, refer to the 

equivalent files in the lib/DEV/BJT directory. The critical files and ones 

most likely to have an error are NPISCitf.h, NPISCdefs.h, and NPISC.c. 

9. For SPICE3d, the NPISC device must be defined in the variables SUBDIRS 

and MSCSUBDIRS in lib/DEV/Makefile. 

10. The user should clean everything and recompile SPICE to make sure that all 

dependencies are taken into account. 



11. PVM has not been tested with SPICE3d and the procedure for adding the 

compilation of npiscslave.c and npicsctrl.c is unknown. One can 

attempt to define the appropriate variables as discussed in Section 17.1.4 on 

page 306 and compile the routines manually. 

17.2 Adding Another Device Simulator 

This section describes how to add another device simulator such that it can be used within the mixedmode 

environment. 

17.2.1 Changes to Device Simulator 

This section discusses the changes required for the device simulator. SPICE determines a bias and the 

mixed-mode interface writes an input deck for the device simulator. The interface executes the device 

simulator using that input deck. In return, the device simulator must perform the following. 

1. It must be able to load a mesh and a previous solution at some DC point or at 

some time instant. An important advantage is to be able to load the last two 

solutions and then use a projection to find an initial guess at the new bias point. 

2. Given a DC bias, a transient bias and a ∆t, or an ac frequency the device 

simulator needs to solve for the current vector and conductance (susceptance) 

matrix. The conductance matrix is for the frequency given or at some low 

frequency value. Refer to “Equations for Device Simulation” on page 269 for 

more information. 

Most simulators posses these attributes except for finding the low frequency conductance matrix in DC 

and transient analysis. The changes to obtain this information is minimal and should not be a major 

problem. 

17.2.2 Changes to Mixed-Mode Interface 

As a basis, one can follow the currently configured Stanford version of PISCES. There are a few small 

changes in a couple of routines and a number of new routines that must be written. All changes are 

specific to the device simulator. 



npiscdefs.h 

This file is used to define the new device simulator and to give it an appropriate identification number. 

This number corresponds to the level given on the .model card. All code specific to that device 

simulator should be surrounded by an #ifdef structure so that it may easily be excluded in a 

compilation. 

npiscexec.c 

The purpose of this routine is to execute the device simulations. SPICE passes this routine the voltage 

boundary conditions on each electrode of the numerical device. This routine returns the solution for 

the current vector and admittance matrix. 

npiscexec calls two subroutines that are specific for the device simulator as determined by the level 

value. One routine writes the input deck for the device simulator and the other reads the solution from 

the files created by the device simulator. For Stanford PISCES, these routines are as follows and are 

located in a “case” structure in the file. 

int NPISCwriteStanford( NUMDEVbias *) 

int NPISCreadStanford( NUMDEVbias *, NUMDEVsoln *) 

npiscwriteMYSIMULATOR.c 

This routine is responsible for writing the device simulator input deck. A pointer to a structure 

containing the information about the bias is passed to the routine. An error code or 0 is returned from 

this subroutine call. 

The bias structure contains information about the SPICE instance name, SPICE model name, voltage 

bias, time step, frequency, temperature, etc. (Refer to numdevdefs.h for all the information 

contained within the structure.) This information should be sufficient to write an input deck for the 

device simulator. 

There are a couple of requirements on file naming conventions. 

1. The solution for the current bias must be saved as: 

[Instance Name].solution.prev0 



Refer to the files npiscmvfiles.c, npiscwritestanford.c, and 

npiscexec.c for descriptions of how these files are manipulated and how to 

utilize these solution files. All routines are well documented. 

2. Every file created must start with the instance name. This provides a unique 

way for identifying each file and avoids clobbering other files. 

3. In “Running a Mixed-Mode Simulation” on page 286, a file naming 

convention is presented. Any new device simulator should follow the given 

convention to avoid confusion. 

The npiscwritestanford.c file can be used as a starting point and modified for the needs of the 

new device simulator. The code is well documented and should not be difficult to follow. 

npiscreadMYSIMULATOR.c 

This routine is responsible for reading the results of the device simulation. When creating the input 

deck, one should have specified output files for saving the current vector and conductance matrix of 

the device solution. Given the pointer to the bias data structure which contains the instance name for 

identification and given a pointer to a solution data structure, this routine reads the simulation results 

and stores them in the solution data structure. It must also multiply by the area factor if it is not done 

during the device simulation. 

The npiscreadstanford.c file can be used as a starting point and modified for the needs of the new 

device simulator. The code is well documented and should not be difficult to follow. 

npiscmethod.c 

In PISCES, there is a card called “method” that is used to define the numerical methods during the 

device simulation. This method is the same for all device simulations for a specific model. Hence, the 

mixed-mode interface has been designed to accept this method card in two formats (Refer to “Method 

and Model Parameters” on page 288 for more information.), store in its internal structures, and pass it 

to the npiscwriteMYSIMULATOR.c routine through the bias data structure. Since other device 

simulators have something similar, this routine is modified to take that into account. 



There are two ways to determine the method line. The easiest way to implement the method card is to 

read it from a file named [Model Name].method which is the default in npiscmethod.c. 

In order to eliminate an extra file, a binary encoded method parameter is added to the SPICE .model 

parameters. Essentially, a binary number (written in decimal format on the .model card) determines 

whether a logical expression on the PISCES method line is true or false. The numdevdefs.h file 

contains defined variables for all the possible actions. Each action has a number in base two that 

corresponds to a bit in a long integer. 

The npiscmethod.c routine takes the integer value given on the .model card and converts that to 

character string for the numerical device input deck. This file and the numdevdefs.h file are well 

documented and the programmer should not have a problem understanding how to modify this routine. 

If there is no method line, everything is initialized to NULL. 

npiscmodel.c 

This file is analogous to the npiscmethod.c file except it does the processing for the model card in 

the numerical device input deck. Refer to this routine and the numdevdefs.h file for more 

information. 

After all changes have been made, the new files can be added to the makedefs file so that they are 

compiled and linked when SPICE is built. Once included, the new device simulator can be used in a 

mixed-mode simulation simply by specifying the proper level on the .model card in the SPICE 

netlist. 


References 

References 

[1] Yu, Zhiping, Robert W. Dutton, and Hui Wang. “A Modularized, Mixed IC Device/ Circuit 

Simulation System.” Proceedings of the Synthesis and Simulation Meeting and International 

Exchange. Kobe, Japan. April 1992. 

[2] McCalla, William J. Fundamentals of Computer-Aided Circuit Simulation. Boston: Kluwer 

Academic Publishers, 1993. 

[3] Mayaram, Kartikeya and Donald O. Pederson. “Coupling Algorithms for Mixed-Level Circuit 

and Device Simulation.” IEEE Transactions on Computer Aided Design. Vol. II, No 8. August 

1992. pp 1003-1012. 

[4] Rollins, Gregory J. and John Choma. “Mixed-Mode PISCES-SPICE Coupled Circuit and 

Device Solver.” IEEE Transactions on Computer Aided Design. Vol. 7, No. 8, August 1988. pp 

862-867. 

[5] Geist, Al, Adam Beguelin, Jack Dongarra, Weicheng Jiang, Robert Manchek, and Vaidy 

Sunderam. PVM 3 User’s Guide and Reference Manual. Oak Ridge: Oak Ridge National 

Laboratory, 1993. 

[6] Johnson, B., T. Quarles, A. R. Newton, D.O Pederson, and A. Sangiovanni-Vincentelli. SPICE3 

Version 3f User’s Manual. Berkeley: Regents of the University of California, 1992. 

[7] Dutton, R. W., F. Rotella, Z. Sahul, L. So, and Z. Yu. “Integrated TCAD for OEIC 

Applications.” International Symposium on Optoelectronics for Information and Microwave 

Systems. Proceedings of the SPIE - The International Society for Optical Engineering. Los 

Angeles, CA. January 1994. 

[8] Quarles, Thomas L. “Adding Devices to SPICE3.” Memorandum No. UCB/ERL M89/45. 

Berkeley: University of California, 1989. 

[9] Quarles, Thomas L. “SPICE3 Implementation Guide.” Memorandum No. UCB/ERL M89/44. 

Berkeley: University of California, 1989.

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